The British-English colloquial, humorous and euphemistic phrase to fall off (the back of) a lorry means, of goods, to be acquired in dubious or unspecified circumstances, especially to be stolen. (The variant with truck came into use later in Australian and North American English.)

Thieves have sometimes pretended that the goods that were in their possession had fallen off the back of a lorry; for example, the following paragraph is from The Essex Chronicle (Chelmsford, Essex) of Friday 28^th May 1937:

Chickens and Implements in Charge.—Robert George Pittkin, 31, bricklayer, no fixed abode, was charged with having in his possession two dead fowls believed to have been stolen, also housebreaking implements, at Chingford, at 1.30 a.m. on May 20.—P.c. H. Coote, said he saw prisoner in Rangers Road carrying two paper bags, which on examination were found to contain two dead chickens. Prisoner said “they fell off the back of a lorry.” When searched, a hammer, two pocket torches, two knives, a bunch of eight keys, a coil of wire, and a length of string were found on him.—Remanded for a week.

There seems to be an early instance of the phrase in the following from a story about Petticoat Lane Market, in London, by Russell W. Baker, the London correspondent for The Sun, published in The Sunday Sun (Baltimore, Maryland) of 16^th August 1953:

‘Off The Back Of A Lorry’
Across the street a swarthy fat man screams his wares—rugs—to an insensitive crowd:
“Every one of these fine Persian rugs a bargain! The lady wants to know how I can afford to sell these fine Persian rugs for less than you’d pay in the West End for a bath mat! The truth rests between me and the constabulary, madam, but I’ll just inform you that the whole batch fell off the back of a lorry last night.”

The fact that the journalist had written the following at the beginning of his article reinforces the probability that the “swarthy fat man” used to fall off the back of a lorry as a euphemism for to be stolen:

Listen to the pitchman: “I’m not going to sell you this beautiful piece of cut glass! I’m going to give it away!”
That’s the cry of Petticoat Lane, but don’t open your mouth too wide to gape, or the gentleman will wind up selling the fillings out of your back teeth.
Want your pocket picked? Go to Petticoat Lane.
Looking for your laundry that was stolen off the truck last week? They’ll gladly sell it back to you at Petticoat Lane. Cheaper than the laundry bill.

The second-earliest instance of the phrase that I have found is from The Arizona Daily Star (Tucson, Arizona) of Tuesday 17^th May 1966, which published ’Enry’s Their Man: Pubsters ’Ave ’Ope [= Have Hope], about Henry Cooper, a 32-year-old Cockney preparing for his encounter with Cassius Clay¹ in the Thomas A. Becket, a pub on the corner of Old Kent and Albany Roads, in London:

They [= the customers] are a motley lot—the Becket is not a family-type pub—of dockers who live in the Southwark neighborhood, sports from all over the southeast of London, and wide boys from anywhere, fellows “on the fiddle²,” always looking for a piece of saleable merchandise to “fall off the back of a lorry.”

¹ Cassius Marcellus Clay (1942-2016), a.k.a. Muhammad Ali, American boxer
² A glossary at the end of the article explains that on the fiddle means “looking for a chance to cheat or manipulate”.

The British playwright Alan Bennett (born 1934) played on the phrase in Getting On (London, 1972):

(George and Enid now sit silent as Polly and Geoff slowly edge into the room.)
Polly: Just wait till you see this!
Geoff: It’s the most incredible thing, George, it really is. Look at that!
George: But it’s a tombstone.
Polly: Well, it was. It isn’t now.
Enid: It’s going to take some cleaning.
Geoff: I’ll give it a wash.
Enid: Where did it come from?
Geoff: Fell off the back of a churchyard.
George: ‘Sacred to the memory of Joseph Banks, who departed this life August 16, 1842. Aged 28 years.’

A variant is to fall off a lorry; on Thursday 13^th August 1970, the St. Petersburg Times (St. Petersburg, Florida) reprinted the following cartoon from Punch, the London satire magazine; a man carrying an antique statue over his shoulder declares to a bobby:

“It fell off a lorry.”