I've done a bit more digging and found some information that may explain the story.
Note the linked article refers to "basic portions of the atomic bomb" and "fissionable materials" being sent to the north west of England not complete atomic bombs. This is important in understanding what I've now found.
Turn the clock back to 1944. The Combined Development Trust, later the Combined Development Agency, was the joint US/U.K. body charged with finding uranium oxide ores for use in the Manhattan Project. One major source was the Belgian Congo and 3 way agreements were signed in 1944/45, Belgium, U.K. & US, for its supply. Some of the raw ore available to the CDT came to Britain and was used in Britain's atomic programmes until 1953. The following article specifically notes that in 1946 some 1,350 tons of uranium oxide ores were supplied under CDT agreements to a plant at Springfield in North West England. That was a new processing facility created to support Britain's civil & military nuclear programmes.
This article sets out the background to what was going on.
From "Churchill's Bomb" by Graham Farmelo, it seems Britain had 5 nuclear sites in the early post-war period:-
Harwell in Oxfordshire - home of a small nuclear reactor and the science of physics, chemistry and metallurgy research.
And 4 plants in North West England including:-
Springfields in Lancashire - extraction of uranium from ores to be turned into reactor fuel.
Capenhurst in Cheshire - enrichment of the fuel produced at Springfields where necessary.
Windscale (later renamed Sellafield) in Cumbria - home to the main reactors and the plutonium extraction facilities to produce weapons grade nuclear materials.
So the Washington Post reports have nothing to do with stockpiling atomic bombs in Britain in 1946. Given that the origin of the reports was a US Senator, Tom Connally, Chairman of the Senate Foreign Relations Committee, I suspect that this was more to do with US internal politics surrounding the passing of the McMahon Act earlier in the year. Was he trying to flag up what he considered to be a breach of it?