Crew can move into management if they want to. My manager used to be crew and there are quite a lot that have recently accepted a secondment to be managers overseeing other crew for a year (or more I expect if they enjoy it).
Obviously you have to go through an interview for any new job in BA but crew are allowed to apply for management roles if they have the skills to do the job.

Incidentally the head of Mixed Fleet used to be cabin crew herself at LGW a few jobs ago!