It depends on the train. I think most Gatwick Express trains have charging ports, but the bog-standard southern ones are hit and miss depending on where you’re travelling. Some of the ones that go through Portsmouth are absolutely ancient.
Not much else to say. Southern railway trains, can i charge my phone without paying for first class?
Do Southern say that all seats in first class on all their trains have charging points?
I don't travel on Southern trains myself; but my experience in general is that some trains have power points and some trains don't. In some case where power is provided at the seat, it's via a standard 13-amp socket rather than by USB connection -- so make sure you have a standard plug-in USB charger rather than just a cable to plug into a USB outlet.
Probably best to carry a charged-up power bank too, as you might not find a socket.