One shouldn't get too concerned about the driving licence issue. An overseas visitor will need an International Driving Permit and that will say what vehicles he is entitled to drive. The classes shown on the IDP won't necessarily coincide with UK or EU categories such as B or BE, etc.
What is not quite clear to me is whether the OP is intending to ship his outfit over from Canada or the buy/rent one when he gets to Liverpool. There may be technical issues regarding temporary importation of vehicles. It would also be important to know for how long he is intending to tour Europe of he is bringing the outfit over from Canada and whether it will be be returning back to Canada afterwards. If the vehicles are going to be bought in England, will they be returning back to the country after the trip and remain there?
What is not quite clear to me is whether the OP is intending to ship his outfit over from Canada or the buy/rent one when he gets to Liverpool. There may be technical issues regarding temporary importation of vehicles. It would also be important to know for how long he is intending to tour Europe of he is bringing the outfit over from Canada and whether it will be be returning back to Canada afterwards. If the vehicles are going to be bought in England, will they be returning back to the country after the trip and remain there?