Quick question re checking bags. I am travelling GLA->LGW->BUD->SKP on Thursday

GLA->LGW EasyJet and LGW->BUD->SKP is Malev Hungarian Airways. Now when I check in at GLA, will I be able to check in for the Malev portion of the trip and check my bags right through? My friends are taking the same trip except starting EDI->LGW. They seem to think we will have to check in at LGW.

What might complicate matters is that we are on a group booking with Malev, so we may have to all check in together at LGW...

I think the same, but maybe someone can shed some light on the matter?

Thanks!