I haven't talked to any with trucks and I've contacted a good handful, so possibly I was assuming? But also, when I ask local friends about truck rentals, they just stare back at me blankly!
We tend to call them "vans". You can hire a Luton van with a lift too if you want, for getting those heavy items up into the van.
We don't tend to have open back trucks, if that is what you were thinking? If it rains, you will be glad of a "van".
Man with a van, can mean two or three men with a Luton. Or you can hire one yourself. Having moved ourselves once before
, I would always hire the labour too now.
My son used two Russians with their van to move (getting across London to a top floor flat with lots of stairs) and they charged £20 an hour. They got a big tip as they worked very hard and were faster than they estimated.
Often your own house contents insurance will cover any breakages; have a look on your policy. So far, I've never had any breakages from "man with a van" and I have moved a lot, but always had breakages from the big named removal firms we used.