As it made it all over Scotland unlikely to be the alternator, but by no means impossible.
Charge the battery fully, but measure the voltage before you do so, then after charging see what effect it has and when running after about 10 minutes measure the voltage again, with all lecky off(engine apart) and will lights etc on, do this at 2000rpm, and make sur eit is holding a minimum of 12.8V with lights etc on.
tabetha