From Roader's Digest: The SABRE Wiki
When the new A1--M1 link road was built in the mid 1990s, completing a high-speed through route between the port of Felixstowe and the Midlands, it was decided to give it a continuous number. The road was made up of the A604 and part of the A45, with some new construction. It should, according to the usual convention, have been an "A5x" road, but no suitable numbers seem to have been available. The number A45 remained with the western section of its original route. A604 was presumably not distinctive enough for such an important road. And so the route became the new A14. (It is worth noting that the A14 falls entirely within Zone 1 of the motorway numbering system).
Junction numbers were provided from 1 to 35 (Cambridge east) during 2001, extended to Felixstowe (Junction 62) in early 2002.