Bikes on trains in the UK

Sorry to revive an old thread! But i'm possibly coming down to London next week to buy and collect a bike, bringing it back on the train. I know i've to read the individual train companies policy and i have done, it will either be East Coast or Grand Central trains, however i was wondering if anyone has ever been turned away from a train even with their advanced booking because they have a bike? It's something i'm quite worried about happening haha, wouldn't really enjoy having to pay out for another train with no guarantee i can get on it.

I would be going from Wakefield - London Kings Cross, if anyone could shed some light on if they've been turned away or anything about kings cross regarding bikes!

Although I've never tried it apparently covering with bin bags makes it luggage not a bike and thus it can be carried , probably won't be a issue though