happy.paul,
Indeed - CAA Medical takes about 1.5 hours although depends on how busy they are and if you pass everything first time.
NATS should pay for your travel expenses as this is part of your training/job requirements. If you can't/won't go to Aviation House before you start at the college, NATS send you for your medical while you're there, so you should be fine. Best call HR to double check though!