Its been nearly twenty years since I've been to Heathrow because I've found by far the cheapest way from Scotland to London is low cost airlines such as Easyjet or Ryanair which use Stansted Airport. Stansted's a long way out of London but even with an hour's train journey and a £25 return train fare from Stansted to London its still cheaper than going the whole way by train and a fraction of the cost of BA or BMI between Scotland and Heathrow. Though if you arrive at Heathrow from a trans-atlantic flight you will just want to pay the premium for the convenience of going direct from there to Glasgow. But allow yourself plenty of time at Heathrow - its a huge airport and it has lots of nice shops.