If this is Operation Buffalo, then a low yield (3 kiloton) version of the 40 kiloton 'Blue Danube' weapon was dropped from 35,000 ft and from a Valiant on 11th October 1956. The aircraft was WZ366 of 1321 Flight, 49 Squadron, piloted by Squadron Leader T Flavell. Both he and the bomb aimer, Flight Lieutenant E Stacey, were awarded the Air Force Cross for their part in the operation.
There has been much criticism of this series of tests, but the original plan, to drop a 40 kiloton weapon to explode at 1,200 ft was abandoned because of worries that the fuzing system might fail causing an explosion at ground level. The 3 kiloton weapon, which functioned perfectly, exploding at 500 ft as planned, was a safety compromise.
Operation Antler, a series of tests designed to perfect the Blue Danube and Red Beard warheads were planned for Maralinga in September/October 1957, but were cancelled when plans were made for the the second phase of the British nuclear programme, the dropping of the first thermo-nuclear megaton weapons in what would be known as Operation Grapple. Maralinga was not a suitable venue, Christmas (Kiritimati) Island and Malden Island were the selected venues instead.
Incidentally the first series of Grapple tests, between 15th May and 19th June 1957, three weapons were dropped dropped from 45,000ft, again by three different Valiants (XD818, XD822 and XD833) of 49 Squadron, exploding at 8,000ft above Malden Island to prevent the fireball touching the ground and causing "excessive radiation problems." Further weapons were dropped in subsequent tests over Christmas Island before the final two were detonated, suspended from tethered balloons. In September 1958 Britain's 'H-Bomb' was available to the V bomber force.
The Valiant was the only British bomber to drop a live nuclear weapon, neither the Victor nor the Vulcan ever did. The ban on atmospheric testing probably ensured this.
Cheers
Steve