Have no truck with
To reject or to have nothing to do with.
We are all familiar with trucks as carts and road vehicles, but that's not what's being referred to in 'have no truck with'. This 'truck' is the early French word 'troque', which meant 'an exchange; a barter' and came into Middle English as 'truke'. The first known record of truke is the Vintner's Company Charter in the Anglo-Norman text of the Patent Roll of Edward III, 1364. This relates to a transaction for some wine which was to be done 'by truke, or by exchange'.
So, to 'have truck with' was to barter or do business' with. In the 17th century and onward, the meaning of 'truck' was extended to include 'association'/'communication' and 'to have truck with' then came to mean 'commune with'.
'Truck' is now usually only heard in the negative and this usage began in the 19th century. To 'have no truck with' came to be a general term for 'have nothing to do with'. An example of that is cited in the Journal of the Royal Asiatic Society, 1834:
Theoretically an officer should have no truck with thieves.
'Trucking' was also country slang for 'courting'/'dallying with' (and no, in case you are wondering, it has nothing to do with any similar word beginning with 'f'). To 'have no more truck' meant that a courtship had ceased. An example of that usage in print is found in Notes and Queries, 1866:
[In Suffolk] A man who has left off courting a girl, says that he has 'no more truck along o'har'.
'No truck with' may seem rather antiquated language now, although it is still used. Even older is a version that hasn't often been heard since Grandma's day - 'brook no truck with'. 'Brook' in this context means 'make use of/enjoy' and adds emphasis to the standard 'have no truck'. The image I have of someone who would 'brook no truck' is Queen Victoria, in her later and more 'unamused' years. A truculent woman at that stage by many accounts, although 'truculent' and 'truck' aren't related.
Going back to the original 'barter' meaning of truck, this also became extended to include the sundry items that were bartered and also small odd jobs or errands. The stores that were set up to service the needs of itinerant navvies while they were building the UK's canals and railways were known as 'truck stores' or 'tommy shops'. The great rural campaigner William Cobbett referred to these in his classic, Rural Rides, 1825:
In the iron country [the Black Country]... the truck or tommy system generally prevails.
The navvies' sites were often far from towns and were the only places that the workmen could shop. The shops were generally ruinously expensive and provided poor quality goods. The workers were often paid in vouchers that could only be 'trucked' at the workplace shop. That all ended in the UK with the passing of the 1887 Truck Act, which made the worst excesses of the truck trade illegal. In the USA such shops were known as company stores and are the subject of the well-known American song Sixteen Tons:
You load sixteen tons, what do you get?
Another day older and deeper in debt.
Saint Peter, don't you call me, 'cause I can't go;
I owe my soul to the company store.
Note: 'Truck shops' and 'truck stops' are only distantly related. The American term 'truck stop' arose independently as the name of the places that truck drivers and their trucks get refreshment.
The alternative name of 'tommy shop' derives from the widely used term 'tommy' which appears in several terms that were coined around the late 19th century:
Tommy Atkins - the generic name of a British soldier of the line.
Tommy rot - referring to the basic rations available in tommy/truck shops.
Brown tommy - rough brown bread available in tommy/truck shops.
Tommy bar - a small spade.
I can find no definition of 'tommy' from the time that these terms were coined, but the meaning of any of them wouldn't be altered much by exchanging it for 'humble'/'unexceptional'.
Truck shops may be a thing of the past in the developed world but, with the advent of e-commerce, trucks now bring the shopping to us.
See also: Fell off the back of a truck.