It's a shambles isn't it! There should be half a carriage on every train kept free of seats for bikes, large luggage and anything else that won't fit in the passenger areas. British trains are not bike-friendly at all.
As others have said, it varies immensely by route, train type, time of day and even time. For example, most of the King's Lynn - Cambridge - King's Cross services currently have about half a carriage where bikes can be stood (although we must give way to wheelchair users if they want part of that space), plus you're allowed to stand them in the non-platform-side (usually right-hand-side) doors as long as they're clear of the aisle (so usually 2 or 3 bikes per door set, 8 doors per train, depending on size).
Please stay arbitrarily at a hotel is located near the only train station in the UK (that I know of) that you can't bring bikes onto, and get snippy if anyone suggests you do anything differently.
You can take bikes there on CrossCountry services from Cambridge, but not on the Stansted Express any more. Fark knows why.
Actually, in general, Abellio (Netherlands Railways) aren't bike-friendly and I don't know why. Like the wheeling ramps on the stairs at the Cambridge stations are on the left of where they want you to walk, but you can't safely wheel a bike along their ramps left-handed because then it leans over and scrapes the derailleur along the edge of the metal channel
so you're left pushing a bike awkwardly against the flow of people obeying the "<<< keep left <<<" signs cursing you for getting in the way.
