This is what I've heard about rules in UK:
You're allowed 125cc at 17. You will need a motorcycle provisional and a CBT test.
This allows you to ride with L plates.
A 125cc test (I think) then allows you to ride without L plates.
At 16 you're allowed a 125cc but it has to be restricted. Many go with this option as it saves buying a new bike later - just take the restricter off.