Which bomber holds the distinction of being the only British bomber to be produced for the duration of WWII?

In numbers only slightly less than the B-17 (Boeing Model 299), the Vickers Wellington, aka Wimpy, holds the record for the longest-produced British bomber. The production ran from 1932 - 1945 and soldiered on for the entire war as first-line equipment, although later in the war, was relegated to secondary roles. It also was produced in greater quantity than any other British bomber, 11,461 or 11,462. By comparison, the Lancaster only had 7,377 made, the Stirling - 2,371; the Halifax - 6,176.

Barnes Wallis, the creator of the bouncing bomb used by 617 Squadron, proposed the use of his geodetic airframe. This was covered in fabric and allowed the aircraft to absorb a phenomenal amount of damage.

In the early days of the war, the Vickers Wellington was called upon to bring the war to Germany. In fact, less than 24 hours following the beginning of hostilities, Wellingtons and Bristol Blenheims dropped bombs on the Fatherland with an initial loss of 2 Wellingtons.

One can find a great wartime film, "One of Our Aircraft Is Missing" on YouTube. This features a Wimpy and its crew and their escape from the Germans using the Dutch underground railway.