I am not sure about this one, but I think the football team means rovers, argyle, city, united, wanderers etc, something which is also the make of a lorry.
I think you may have misunderstood me. This is just my thoughts but I dont think you should be looking at the name Bedford. I think you should be looking at the second part of any football team's name, i.e. city, united, rovers, argyle (as in Plymouth) etc. Somewhere one of these words could be the make of a lorry. I could be on the totally wrong line of thought though with this. Just in case you do not know, the pubs do not have to be in Lincolnshire.
Albion goes with my initial train of thought then; and Argyle might fit too. Still stumped with the Volunteer. Was looking for Volunteer Soldier, thinking that soldier sounded like shoulder which is upper arms but havent been able to locate such a name.