my guess is the simplest way to do it is to throw away your rail pass, fly london to prague, prague to brussels (paris has no cheap service) and then train to paris.

easyjet flies from gatwick to prague and it can be cheap

brussels air from prague to brussels www.flysn.com is more but isn't ridiculous.

but under almost any condition, if you really want to do it, the easiest thing to do is fly from london to prague and then if you want pick up a train back to paris.