My partner and I travel regularly on the Southern Rail system, with no hassle, just check that they are not doing any rail works, depending how many carriages makes up the train depends whether there are 2,4 or 6 cycle spaces, but you can put your bike in the door spaces at any other point in the train, however if the train passes through Gatwick airport I would opt to board the train either in the front or rear of the train as at Gatwick during the summer the travelling masses tend to crowd into the Middle carriages.