Any Goods Vehicle Testing Station will carry out a voluntary check of your pre 1960's truck, for your own peace of mind on any work you may have done. They will charge you for it according to what you ask them to check. For example you could have just a brake test, which will get you a computor print out showing how well, or not, your brakes performed (at the time of test). On the other hand you could opt for a full inspection which will be done to the same standard as for an MOT.
However, for a pre 1960 vehicle they would not normally issue an MOT because your old truck is unlikely to conform to the current regulations. Hazard lights for one, were not required back then, but now they are, so unless you have retro fitted them recently you wont get an MOT. No MOT means no plate, so no using it for anything other than social, domestic or pleasure.