As far as i'm aware you can ride a 50cc on your car licence, for a 125cc you need to do a CBT (1 day ~ £100) you then can ride a 125 on your own with L plates on for 2 years, if you don't pass your test in that time then you need to do the CBT again.
Direct access around here is around £650 that's CBT, lessons, test, and theory test/books etc. If you may go for anything above 125 then its the only way to go, if you're going to stick at 125 then the 650 is ~ 12 years riding's worth of CBT's, although i'd like to bet with a full class A insurance would be cheaper.
You could always do your restricted (a2) licence, this lets you ride up 33kw? that's basically a restricted 600cc, then after 2 years you USED to be switched over to a full a class but things may bell have changed since I did my test so worth checking.
So far as 250cc being the max as you said, some 600cc are designed (detuned, for comfort/commuting), so i'd say slower than some of the 2 stroke 250cc bikes of yesteryear, and certainly more comfortable!!!