I'm guessing one of the major considerations in the Lancaster selection was the 17 foot length of the original "Thin Man" bomb. The length was dictated so the plutonium "bullet" could pick up adequate speed before reaching the "target". In order to carry the weapon the B-29 had to be modified by removing part of the bulkhead under the main wing spar and some oxygen tanks located between its two bomb bays, resulting in the "Silverplate" B-29.
Due to impracticalities of a gun type plutonium bomb (it was found the barrel would have to be of a length far exceeding the original 17 foot weapon length), development of the implosion type was seen as the only workable method, resulting in the "Fat Man".
esa-aardvark, details for the British Washingtons are listed here, the British didn't have an atomic weapon available for carriage at the time as far as I'm aware.
Washington to the RAF