I’ll hazard a guess and say going by that list of companies your from Southampton?? If so try Gregory’s in nursling and Freightroute in Eastleigh. Freightroute don’t even give you a driving assessment and they recently had a pay rise. Not great money but palletised multidrop is probably the best experience you can get imo. I was there for 2 months after getting my class 1, set me up perfectly to breeze my assesment for where I’ve been since.
I was a bus driver and loved it but you do get abuse daily. And I mean full on proper mental and physical abuse.