From the UK piont of view - (EU is probably the same) -
The UK does not require Carnets - so no problem on this point.
You are allowed to bring a foreign registered, personal, vehicle into UK, as a tourist, for a period (6 months?) without formality or even documentation other than proof of registration in your home country. Insurance will be a necessity though.
Did you ride through the Green (nothing to declare) or Red (something to declare, or a query) channel where you entered? If the latter, they would have advised you if you were doing anything wrong.
Therefore leaving UK, by any route/method, should be no problem.
Police, in road checks, can ask you to prove your right to ride a foreign registered bike, its legality as far as insurance etc, and that you are within the time limits.
They do this increasingly in London where it appears many "immigrant visitors" ride/drive vehicles far beyond the time limits, ignore parking rules/tickets and often without valid UK insurance. When they find them they CRUSH 'EM !! No question. No argument.
A straightforward visitor has nothing to worry about.
Enjoy all the UK has to offer - particularly 'proper'

!