There are a fair number of flights from Birmingham to London though, and that is around a 2 hour train journey.
Flights between Birmingham and London, are you sure? A quick google tells me I need to go via Dublin! And checking arrivals/departures at Birmingham also shows zero to or from London.
Unless you meant Manchester, which is about 2¼ hours by train from London, so about as far as you're likely to get in the UK within the stated time period. So it would affect one destination. You would still be able to fly London to Newcastle, Edinburgh, Glasgow, Aberdeen.
Glasgow to London (x4 airports), Southampton, Manchester, Bristol, Inverness, numerous islands.... just for example.