Hoofie, the train from LHR to Glasgow is fine if you have to. Heathrow Express to Paddington, Circle Line (or a taxi if you've got a lot of luggage) to Euston/Euston Square, train direct to Glasgow. There are variations involving different combinations of underground to get to Euston. Depending on how many children you have with you ask the ticket vendor if it's worth your while buying a Family and Friends railcard for the journey: you're spending enough that the (immense) discount might cost in on a single return journey.