You can check your baggage all the way through if it is on a single booking. The problem is when you book LHR-BUD and then book ABZ-LHR to meet the BUD flight. In that instance they won't transfer your baggage automatically.
Connecting flights booked as such are still the same as ever and your bags should be tagged the whole way through so you check in at the start and only see them again at your destination (if you're lucky).