It would be a long day, but Megabus can get you there and back for £19. You'd have to do the tube to and from the ground, but that's no big deal.
Problem is the times.
0615 from Liverpool One Bus station gets in to London Victoria at 1230, sleep on the way down.
Coming back is an issue, leave at 2345, get back at 0450.
Cheap and cheerful though, just stuck in London for a while.
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