The earliest printed versions of 'fell off the back of a lorry' come surprisingly late - like this early example fromThe Times, 1968:
"The suggestion of the finder, a casual motorist, that the records 'must have fallen off the back of a lorry'."
There are many anecdotal reports of the phrase in the UK from much earlier than that, and it is likely to date back to at least WWII. It's just the sort of language that the 'wide-boys' or 'flash Harrys' who peddled illegal goods during and after WWII would have used. These were exemplified in plays and films by the actors George Cole, Sid James, etc. I'm sure a thorough scan of the scripts of the post-war Ealing comedies would throw up a pre-1968 example.
Having been brought up in the truck-free UK with the 'fell off the back of a lorry' version, I have to now concede supremacy to 'fell off the back of a truck'. Versions of that from both Australia and the USA predate the English examples by many years. The earliest that I can find is from the official record of debates in the Australian House of Representatives - Hansard, 1928:
"We heard, through something that had fallen off the back of a truck onto a reporter's table."
In the USA the expression is found just a few years later - as in this example from The Tuscaloosa News, February 1937:
Many transients in Manhattan are constantly being trimmed by suave 'chauffers' in light delivery trucks who whisper confidentially that there are some bolts of cloth in the rear seat which fell off the back of a truck.
The meaning seems to have changed slightly since the phrase was coined. Almost all of the early references cite it as being used as patter in a scam to sell the unwary shoddy goods. The current usage is as a reference to a straightforward 'nudge, nudge/I won't tell if you won't' sale of stolen or smuggled goods.