BA ABZ and GLA flights leave from T5, and with special assistance it ought to be possible to manage collecting bags and checking them back in.

However you've answered your own question in that if it's not possible to collect bags at LHR you're going to have to do what it takes to get them checked through to final destination. This ought to be possible given the single PNR. Is this a Loganair or BA ticket? Most of the advice you'll get here will be under the assumption it's BA with an LM tagged onto the end possibly under a BA codeshare, which would simplify things for the agent.