The law used to be different for learners with sidecars at one stage, with them being able to use higher cc bikes on L plates, I dont know if that is still the case or if indeed it has anything to do with your intial question
Showing your age their Kitch! Yes this rule apparently still stands but Learners who wish to ride a side-car outfit can do so with a power to weight ratio not exceeding 0.16kW/kg and the bike can not be rated over 14 BHP and no more than 125cc.
That said but no 19 yr old superbiker will want to lose his street cred with a Motorcycle Combination.
Quads I thought came under the rules of trikes? Bikes you need to pass your test and depending on what you take your test on restricts what you can ride. According to DVLA...
There are two types of full motorcycle licence:
A light motorcycle licence (A1), which restricts riders to any bike up to 125 cc and a power output of 11 kW. The practical test must be taken on a bike of between 75 cc and 125 cc
A standard motorcycle licence (A), is obtained if the practical test is taken on a bike of over 120 cc but not more than 125 cc and capable of at least 100 km/h per hour. After passing the standard motorcycle practical test, you will be restricted for two years to riding a bike of up to 25 kW and a power/weight ratio not exceeding 0.16 kW/kg. After this you may ride any size of bike
on top of this you have category P which is Moped.
Oh Kitch - Now a days mate you don't need the guy in front with the flag either.