Originally Posted by corporate-wage-slave

Yes, follow the purple signed to Flight Connections T3 down to a small bus station by the T3 apron. A dedicated bus service then takes you on quite a long hike around the airport, including a 1 km tunnel. Takes about 12 minutes, service frequency every 6 minutes. Then you go up to Flight Connections UK and Ireland T5 to pass the UK Border there, and up to the usual security scan in North. It's well signposted so I can give more detailed instructions but it basically boils down to "follow the purple signs to Flight Connections then Flight Connections T5". If you know T5 well then you can exit the UK Border in T5 and re-enter via South, but I'd not recommend it if you are a novice.

Just present your GLA boarding pass at MRS and ask for it to be checked through to GLA. That will do the necessary.