The older trains on my route are fine (don't ask me which, I'm not a spotter), a Brommie fits perfectly into the rarely used luggage slot between the sets of backwards and forward facing seats (must be the same trains as the East Anglia line mentioned above), so a busy train isn't a problem (more so since I start and finish my journeys at the ends of the line). On the newer trains, it's bit more of a pain, there's a single seat where you squeeze one in by its side (only one though, there's another single seat which looks the same but doesn't quite have the space), otherwise it's under the table (you will lose some paint), on a luggage rack, or by the doors. Some trains have fold-down seats in the vestibule. I wouldn't lock a bike anywhere where it might impede exit on emergency.
The plus side on the new trains is that they have often have a pointless first class which few people realise doesn't apply on metro routes, so even on busy trains there's usually a near empty half carriage. You can't guarantee that the train will have one though, so it's a bit of a lottery.