The dummy device was being flown to Orford Ness, a top secret military test site in Suffolk, in the early 1950s.
It came loose in the bomb bay while over the Surrey town, about 20 miles from London, but the bomb doors held.
An engineer who worked on the device said it was then dropped in the Thames estuary, where it remains to this day.
Fortunately, the device contained no explosives or nuclear material.
The revelation is made in a BBC Four documentary, Britain's Nuclear Bomb: The Inside Story.
Reg Milne, of the Royal Aircraft Establishment, told the programme: "One flight to Orford Ness, a bomb came loose over Dorking. It fell off its hook.
"Luckily the bomb doors were strong enough to hold it."
He revealed: "The pilot took the aircraft over the Thames estuary, opened the bomb doors, and the bomb fell out."
He said the huge splash that resulted nearly drowned a couple of sailors nearby.
"They never found it - it's still in the Thames somewhere," he added.
The programme features interviews with military veterans and scientists who took part in the atomic bomb programme, some speaking for the first time, plus newly released footage of the British atomic bomb tests.
At the time, with the UK excluded from the US nuclear programme, scientists were scrambling to make a British bomb and seemingly cutting a few corners in the process.
According to the programme, highly radioactive plutonium was also frequently transported in a lead-lined box by car from the research reactor in Cumbria to a testing site in south London.
On one occasion, the vehicle broke down and the driver had to knock doors to get help.
As a result, the dangerous material allegedly spent several hours in the boot of a Vauxhall stranded in a pub car park.
Britain's Nuclear Bomb: The Inside Story will be broadcast on BBC Four on 3 May.
Scientists working on the UK's first atom bomb narrowly avoided a fiasco when they nearly dropped a five tonne replica on Dorking, it has emerged.