If you don't have any joy with London flights, you could also consider flying to Birmingham or Southampton. Both have airport stations, with links to London taking 1h14 and 1h11 respectively, and generally pretty speedy processing. Fares aren't necessarily cheap unless you can pre-book, though.

The day train from the Sneck takes ages - nearly 8 hours. It's comfortable enough, but slow enough that you get no advantage over flying.