I had this happen to me a month ago but I didn't want to risk it, so didn't find out myself what would happen in such a case.
I had two single advance tickets with Virgin Trains. One in the morning to London Euston and one in the evening from London Euston.
So what happened is me and my friend were in zone 3 and we decided to head back to London Euston about 1-1:30 hour before our train departure time and we would have made it there (based on the app that I used to find directions) but when we went to board our overground train they told us we won't be able to make it to London Euston as there was an accident or some other problem and that our overground train could only get us to the next station as the issue was on/after the next station (and we needed to do about 4 stops to make it to the underground station that would take us to London Euston) and so they told us we would have to take a bus to the nearest tube instead, which we did but obviously got late for our train (bus in traffic probably took most of the journey).
I wasn't sure if in such a case we would be entitled to use another train (we even missed the next one as that one was in 10 mins after ours). I think we probably would be allowed if we were travelling on National Rail trains and got delayed on them but this was just an overground train (that we had a separate ticket for).
So as soon as I knew we (me and my friend) were 100% late we stopped traveling to London Euston and went to the Victoria Coach station to get on a megabus (not the most pleasant ride but it was about £16/person whereas we would have to pay ~£90/person if the inspector on a train would ask us to buy a new ticket).
But I'm still curious by this day what would happen if we were to use a later train that we were supposed to with our advance tickets?
P.S. Apologies for the long post.