I'm in England so the process is slightly different here, but mostly similar. There is no requirement for a physical exam prior to referrals to either your CMHT or a GIC. You won't need a physical exam of the type I'm thinking you're referring to at any stage other than if you eventually go for surgery which requires it, hysto or bottom surgery for example. They will have to look at your chest briefly if you choose to have top surgery just so they have an idea of what they're working with prior to starting, and again to mark you up. A lot of places require a groin swab for MRSA prior to top surgery as well, but that's normally just up the leg of your boxers, not taking them off.
Explain that you've been in touch with Glasgow and that you need a referral to the CMHT in regards to getting referred on to them. If you have issues with that it's often a good idea to suggest they contact Glasgow themselves as some GPs can be unsure of what they should be doing if they haven't dealt with it before, but most have now seen a trans person before, so it shouldn't be too bad.