South-West Trains have bike bans in the morning rush-hour for up trains to Waterloo and in the evening rush-hour for down trains from Waterloo. This does not apply to foldaway bikes, which don't take up any more room than a moderately-sized bag. This makes sense as trains can get very crowded, and a bike not only takes up a lot of space, it also is hugely obstructive when a train is crowded.
SWT stock does have a row in one carriage per four-car set of fold-up seats which is to be used for bikes. However, if people are already sitting on them, then this can cause a problem if someone boards with a bike, as the bike will then have to be kept in the vestibule by the doors. If more than a couple of people have bikes, then other vestibules have to be used.
The biggest problem I've found when taking my bike up to London is that afternoon services can get pretty crowded, and bikes are inconvenient for other passengers, far worse than baby-buggies and luggage. Late-night trains can sometimes be short (one four-car set rather than two), and also can be quite crowded. I find the best thing is to be as considerate as possible to other passengers when taking a bike on a train, and some sort of compromise is normally worked out.
One useful thing about SWT is that they have reduced the number of seats on the 455 and some of the 450 class sets, and this makes it easier to travel with a bike. Of course, back in the days of Mark 1 stock, the guards would allow me to put my bike in the luggage compartment; those days have gone, and it is also true that for most of the time the luggage compartment stood empty, parcels traffic being a thing of the past, and thus reduced the number of seats per train.
Altogether, although I find taking my bike up to London on the train is convenient for me -- I live too far out to cycle into Central London -- bikes and trains don't mix easily when the latter get crowded. Even if official bike space is made available on all stock, it would in any case soon get filled by standing passengers in a crowded train. There are no easy answers; I find that it's best to try and sort out things on an informal manner, most people are reasonable enough.
