A bigger LHR will take more routes that go via Manchester & Birmingham. You just have to look at the loss of routes over the last year to see airlines are desperate to keep slots at Heathrow. The sensable system is to auction slots at Heathrow so that airlines use them as if it cost money. We may then get a move to more direct flights from the likes of Mancester.
I cannot see the third runway getting the green light. MPs from London are not keen and it does nothing for MPs from the North. The way to make LHR work better is to run a few less flights added with more direct flights from regional airports.