I used to run a railway station, Joko. I must have had to answer your question hundred (if not thousands) of times!
If you've got an 'Advance' ticket, which specifies which train service you must use, your ticket is ONLY valid on that service (and, if you're allocated a reserved seat, ONLY in that seat). If you try to travel on a different train, it will be regarded as if you've got no ticket at all. That means that (on most routes out of London) you'd have to pay a £20 penalty fare (or double the maximum standard fare, whichever is the greater) just to get to the next station at which the train stops at. At that station you could either get off (and seek an off-peak fare to your destination on the next train) or remain on the train that you're already on but pay the FULL fare (without any off-peak discount) to get to your destination.
However,if you've got a normal ("walk up") 'Peak' ticket, you'll be able to travel on any train (even if you've been allocated a reservation on your original choice of service). Similarly, if you've got a normal 'Off-Peak' ticket you can travel on any service during off-peak hours (which generally means after 7pm for services ex London but you should check the rules for your route).
Chris