I think OldGit is right to an extent. People will travel virtually any airport as long as the flight is going to where they want to go at a price they want to pay. Often that price is as low as possible although they may also go on whether they have heard of the carrier!
Personally I will also factor in the door to door time, and indeed the cost of parking etc but many don't.
Getting to an airport by train is inconvienent for most unless they are coming from the centre of the city it serves, or are on the mainline that serves that airport. So you might get the train to Gatwick if you are on a direct service to the airport, but if you have to change, driving becomes a more favourable option.
Incoming tourists don't have so much choice though, they either have to travel by train (or other public transport) or hire a car. So the benefit of good public transport depends on whether you are intending to mainly ship residents of the UK out, or tourists in.