Mavis Batey vividly recalls the V-1 rockets and the means by which the codebreakers at Bletchley Park sought to thwart them. "We were working on double agents all the time, giving misinformation to their controllers. And because we could read the Enigma, we could see how they were receiving this misinformation. One of the things when the Vls started was that the double agent was asked to give a report to the Germans on where the rockets were falling. Because of course they were wanting them to fall on central London.

"At that point, the bombs werefalling in central London so intelligence here wanted them to cut out at a different point. So this double agent was instructed to tell his masters that they were falling north of London. The result of this was that the Germans cut the range back a little and as a result, the rockets started falling in south London. Just where my parents lived."

In this case, it seemed that to Mrs Batey at least, ignorance was preferable to any other state; for security reasons, she knew nothing of this double-cross operation, or the messages that confirmed its success. "I had no idea and it is just as well that I didn't. So when I saw the devastation at Norbury, I did not know that it had anything to do with anything I was doing. It really would have been a terrible shock to know that."

Dilly himself always slept in the office, going back to Courn's Wood once a week. His driving was worse than ever. His mind was totally elsewhere. Fortunately he drove slowly. "It's amazing how people smile, and apologise to you, when you knock them over," he remarked.

In time the buildings inside the Park walls extended into blocks of huts and cafeterias, and by the end of the war the personnel numbered more than seven thousand, increased by observers and liaison men and important visitors in uniform. With all this Dilly had nothing to do. At first his department consisted of ten people, though these included, besides Peter Twinn, two very brilliant and sympathetic young women, Margaret Rock and Mavis Lever (now Mrs Batey). They were accommodated in a small cottage overlooking the old stable yard.

He would, however, need more ciphering clerks-not the vast numbers which eventually made the Treasury complain that "Bletchley was using up all the girls in the country," but still, a section of his own. Into this task Dilly entered with quite unexpected enthusiasm, and when the assistants arrived down from London with the files they were surprised to find him surrounded with pretty girls, all of them, for some reason, very tall, whom he had recruited for the work. The girls took from four to six months to train, though this was not undertaken by Dilly, who never trained anybody, but by a capable and understanding woman, Mrs Helen Morris. They worked on the equations in three eight-hour shifts, and when Dilly wanted to speak to them or to the punch-card operators who registered the encipherments as dots, he would limp across from the cottage, often in his grey dressing gown, indifferent to rain and snow, to tell them his new idea.

Keith Batey, who died on August 28 aged 91, was one of the leading codebreakers working on the German Enigma machine ciphers at Bletchley Park during the Second World War.

Batey was among the first mathematicians to be recruited to work in Hut 6, the section of the Government Code and Cipher School which broke German army and air force Enigma messages. He later moved to the ISK section, which broke the Enigma messages of the Abwehr, the German military intelligence service.

The initials ISK stood for Illicit Services (Knox) – after Alfred 'Dilly' Knox, the brilliant codebreaker who had broken the Abwehr Enigma before dying of stomach cancer in 1943. ISK became operational early in 1942 and finally expanded into a staff of more than 100. Four European Abwehr networks were targeted by ISK: two in the West and two in the East.

Batey himself was responsible for some important breakthroughs in decrypting the Abwehr Enigma system, helping MI5 to control the entire German espionage network in Britain. The intelligence was crucial to the Double Cross system – under which MI5 turned German agents sent to Britain and used them to feed the Abwehr false information – as it showed that the information was being accepted as genuine; it further revealed what the Germans did and did not know about the D-Day invasion plans.

The Allies were able to use the double agents to "reveal" to the Germans the presence of a bogus US army group stationed in East Anglia and south-east England that was to land in the Pas-de-Calais. As a result, Hitler kept two German divisions that had been destined for Normandy in the Calais area.

John Keith Batey was born at Longmoor, Cumberland, on July 4 1919. His father, John, had been invalided home from the Somme; Keith's mother, Elsie, had to support the family on her wages as a part-time teacher.

Keith was educated at Carlisle Grammar School, from where he won a state scholarship to read Mathematics at Trinity College, Cambridge.

Another scholar at Trinity, Gordon Welchman, had been recruited to work for the Code and Cipher School, which had moved to Bletchley Park on the outbreak of war. Welchman was one of the brightest of a number of mathematicians recruited by the head of Bletchley Park, Alastair Denniston – a policy that initially horrified the classics scholars (like Knox) who then dominated codebreaking.

Selected to lead a new team working on German army and Luftwaffe Enigma machine ciphers, Welchman returned to Cambridge in June 1940 to recruit more mathematicians; among them was Batey.

While he relished the intellectual challenge of working in Hut 6, Batey felt guilty that, while so many of his contemporaries were fighting, he was reserved for what he saw as a "cushy" job. In 1942 he decided that he wished to play a more active part in the war.

Accordingly he told his bosses that he wanted to train as a pilot, only to be informed that no one who knew that the British were breaking Enigma could be allowed to fly in the RAF, the risk being that he might be shot down and captured.

Batey then suggested that he join the Fleet Air Arm, flying over the sea in defence of British ships, arguing that he would be either killed or picked up by his own side. Worn down by his persistence, his superiors reluctantly agreed.
On his solo flight during training, Batey came in to land so low that the examiners had to dive to the ground to avoid decapitation. None the less, he passed – probably because of the desperate need for new pilots.

Batey was due to go to Canada for the Fleet Air Arm advanced flying course in late 1942, by which time he was engaged to Mavis Lever, a young female codebreaker who was working with Knox. Batey and Mavis had met when he helped her to solve a complex cipher problem. Mavis later recalled: "I was alone on the evening shift in the Cottage and this time I sought the help of what Dilly called 'one of the clever Cambridge mathematicians in Hut 6'; as luck would have it, it was Keith Batey. We put our heads together and in the calmer light of logic and much ersatz coffee solved the problem. Perhaps Welchman had a point when he said that 'the work did not really need mathematics but mathematicians tended to be good at it'. Dilly made no objections to my having sought such help and even took it in his stride when, after a decent interval, I told him I was going to marry the said 'clever mathematician from Hut 6'. He gave us a lovely wedding present."

The couple married in November 1942, shortly before Batey left for North America. Batey's Fleet Air Arm career never progressed any further. He was seen as being more valuable at Bletchley than flying naval aircraft, and was ordered back from Canada to work in a new section working on the Abwehr Enigma.

Knox, having made the initial breakthrough into the machine which was used for high level communications between the Abwehr in Hamburg and their stations in occupied Europe, was now terminally ill. Batey, working alongside his new wife, enjoyed a number of successes of his own. In August 1943 he solved the Enigma ciphers of the Sicherheitsdienst, the Nazi party's own intelligence service. Three months later he cracked the cipher used by the Spanish military attachés in Berlin and Rome to report back to Madrid on German and Italian military plans and assessments.

He would subsequently go on to write much of the official history of the ISK section, which has still not been released by GCHQ.

Batey had a formidable intellect which could alarm some of Bletchley's less exalted staff. In her biography of Dilly Knox, Mavis Batey recalls: "[Keith] tried to give a newcomer a tutorial on how the machine worked technically and afterwards she fled, never to be seen again; it was rumoured she had a nervous breakdown."

After the war Batey passed the Foreign Office examination. He served in the high commissioner's office in Ottawa from 1947 to 1951 and then as private secretary to Philip Noel-Baker, Secretary of State for Commonwealth Relations.

He was transferred to several other Civil Service departments, one of which involved dealing with guided weapons, and in 1955 was appointed Secretary of the Royal Aircraft Establishment at Farnborough, working there for 12 years.
In 1967 Batey spotted an advertisement for the post of Secretary of the Chest at Oxford, the university's financial officer. He got the job, and five years later was invited to become Treasurer of Christ Church.

On his retirement in 1985, he was presented with bookshelves made from the original timber of the frame of Great Tom, the bell in Tom Tower, which sits over the main gate to Christ Church and was designed by Sir Christopher Wren.

He was recently asked to contribute to a forthcoming history of his alma mater, Portrait of Trinity – an enterprise to counter the damage done to the college's image by its having produced four members of the so-called Cambridge spy ring (Kim Philby, Guy Burgess, Anthony Blunt and John Cairncross).

Batey was able to reassure the college that it had also made a positive contribution to British intelligence operations, with five of the leading codebreakers – Welchman, Stuart Milner-Barry, Bill Tutte, Rolf Noskwith as well as Batey himself all having been recruited while at Trinity.

Batey retained his faculties to the end. Given the standard compos mentis test by his doctor shortly before his death, he answered every question correctly and then said: "Now, young man, what do you know about Fourier analysis?" before proceeding to give the startled doctor a lecture on the subject.

Keith Batey is survived by his wife and by a son and two daughters.