I am going away and flying from London Heathrow?

I think the trains from Sheffield go into St Pancras. Get the underground from there to Paddington and get the Heathrow Express (it takes 15 mins) to Terminal 4. If you think that's a bit expensive take the Piccadilly Line all the way from Kings Cross St Pancras to Heathrow Terminal 4 (it takes a long time as there are a lot of stops).