The messages were typed into a Lorenz SZ40 teleprinter to be immediately enciphered and sent over the ether to another machine which automatically deciphered them and printed them out as plain text.
This was a far more complicated mechanism than the famous Enigma cipher machine, since the Lorenz SZ40 had 12 wheels compared with the three or four on the Enigma.
It also led to Bletchley Park's other great achievement, the construction of the world's first semi-programmable electronic computer, Colossus, which was used to decipher the Tunny messages.
Tutte was a young chemistry graduate working in Bletchley Park's research section when he was asked to examine an enciphered message, known as Tunny, and its plain text equivalent.
A mistake by a German operator on a teleprinter circuit between Athens and Berlin in August 1941 had allowed John Tiltman, Bletchley Park chief cryptographer, to break one message. But in order to break code continuously, it was necessary to know how the machine worked.
The teleprinter's transmission system used the standard Baudot five-bit teleprinter system, a binary code in which each letter is made up of a series of five elements, or "bits". This consisted of either a "mark" -- the equivalent of the binary 1 and denoted by a cross -- or a "space" -- the counterpart of the binary 0 and represented by a dot. Transmission was by separate negative or positive impulses.
Tutte painstakingly wrote out vast sequences of the individual bits that made up the enciphered and plain text equivalent of the message by hand, looking for some form of pattern. After writing out the first elements in sequences of 41, he noticed various patterns that were more than random and deduced, correctly, that the first wheel had 41 teeth.
Over the next two months, Tutte and his colleagues worked out its complete internal structure and how it operated, right down to the intermittent movement of the second row of wheels. Given that no one at Bletchley Park had any idea what a Lorenz machine looked like, his achievement was regarded as a near miracle.
Tutte, however, remained modest about his feat. Initially, the codebreakers broke each message painstakingly by hand. Then Max Newman, another academic working on Tunny, suggested that ideas for a computing machine put forward before the war by another codebreaker, Alan Turing, could be adapted to the Tunny problem.
The result was a machine known as Robinson, after Heath Robinson, the cartoonist who designed fantastic machines.
But it was unreliable, and long conversations involving Turing, Tutte, Newman and Tommy Flowers, a Post Office telephone engineer, led to the birth of an electronic equivalent, known as Colossus, which ensured access to the highest grade intelligence.
The son of the gardener and cook at Fitzroy House, the Newmarket racing stable, William Thomas Tutte was born on May 14 1917. He was sent to the Cambridge and County High School before going to Trinity College, Cambridge, where he studied natural sciences.
His first year brought him into contact with three other undergraduates who shared his wonder at the natural world and went on to distinguish themselves in various fields -- Leonard Brooks, Arthur Stone and Cedric Smith.
Together they published a paper on how to subdivide a square into smaller squares of different sizes, which provided useful pointers on how electrical circuits could be studied. This solution prompted Tutte's tutor to recommend him to join Bletchley Park.
After the war, Tutte returned as a fellow to Trinity where he worked on his matroid theory, which involved a mixture of algebra and combinatorics, the science of counting. On achieving his doctorate, he accepted an invitation to join the University of Toronto from H S M Coxeter, FRS, the great geometer.
Thirteen years later, he became Professor of Mathematics at the University of Waterloo, Ontario, where his presence helped to attract high-calibre mathematicians from all over the world.
He continued his work on graphs; one important contribution, which he made with Hassler Whitney, was on the question of how many colours were needed to colour any map, which had puzzled scientists from the 1850s to the 1970s: the answer was four.
Part of the attraction of Waterloo was the prospect of returning to the kind of village atmosphere in which he had grown up. Tutte settled at West Montrose, a hamlet outside the city, opposite a celebrated Kissing Bridge, and became an enthusiastic gardener.
His books included Connectivity in Graphs (1966), Introduction to the Theory of Matroids (1971), Graph Theory (1984) and a memoir about his life in mathematics Graph Theory as I Have Known It (1998).
The possessor of an encyclopedic knowledge of British history, Tutte differed from many mathematicians in having a strong interest in literature, in particular detective stories and Sir Walter Scott.
In 1949, he married Dorothea Mitchell, a keen hiker; and, almost until the end of his life, he continued to out-walk colleagues 20 years younger. After she died in 1994, he returned to Newmarket, where his family lived, but he eventually decided a university environment was more suitable and went back to Waterloo.
Tutte was appointed FRSC in 1958, FRS in 1987 and OC in 2000.
(Filed: 09/05/2002) © Telegraph Group Limited.