I'm Gonna rewire my Fender 50's Classic Player Stratocaster because I'm going to need to do it at some point so I might as well do it now.

Anyway, will the sound drastically improve, slightly improve or not change at all (If done right)?

Also, can you recommend me some wiring kits (with links), preferably from UK sites but from anywhere else won't do any harm.

Just wire it better, or change the wiring configuration?

If it's badly wired, you will have a weaker signal and also loose some top end.

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Who's Andy Timmons??
They have a few wiring kits, honestly though I can't imagine the wiring on the classic players are too bad.