This question is just for curiosity, rather than for anything practical.
Is there any railway station in the UK from which it is not possible to get to London with only 1 change? The obvious candidates for a station like this would be far north/west Wales (but the branch lines either meet the North Wales Coast line, or have direct trains to Birmingham), or Scotland, but I can't see any lines which don't offer a direct service to a mainline.
As pointed out in the comments, trains from the Isle of Wight (and also Northern Ireland) fall in to this category! It would be interesting if we limit it to mainland though.