The Virign Atlantic Apprenticeship takes you through the B modules so Im not sure if the Monarch one is the same, It's worth applying for it all the same and trying.
Best thing to do regarding GA is trying to get around the local airfields during the week if possible (as many GA Maintenenace Hangars are not open at the weekend) and start asking some questions get your name out and explain your situation, where abouts in West Mids are you?