Heathrow Express

This Route goes to London Paddington to Heathrow terminals 5

 

This route will have the class 387 trains

 

Damn this is so informative

 

Unfortunately the Heathrow spur from Hayes and Harlington is owned by the airport itself and is operated under license by GWR and Elizabeth Line, but the airport is very very unlikely to allow a license for the route to be made, so a common suggestion, but very unlikely to ever happen