The answer from @Muzer is very good, but I wanted to add what I've learnt as I progressed my negative experience through the system. Train tickets in the UK are confusing, and some of the train operating companies appear to be misleading customers. The devil really is in the detail! If in doubt, ask!
The National Rail Conditions Of Travel 2016 makes it abundantly clear that if you are using an Advance ticket, and you miss your booked train because a previous connecting train service was delayed then you are entitled to take the next train service with whom you are booked with. Obviously, I have to have been at the station at the start of my journey in good time, and I have to have allowed the Minimum Connetion time for my interchange station. In my case, I was booked on a Virgin Trains service to Crewe with an Advance ticket, and my connecting service Southern train was delayed, so I missed my booked train.
National Rail also produce a Guide To Tickets, which clearly states the position in the section on Advance tickets:
"However, if you miss your service because your
connecting train was delayed you will be able to
travel on the next service provided by the same train
company, or any additional services as authorised by
rail staff, without penalty."
National Rail's website, in the section on Advance tickets, clearly states:
"If delays occur while travelling, you will be allowed to take the next available train(s) to complete your journey."
Finally, National Rail have a section of FAQs about Advance Tickets for internal users. The guidance is that if the customer is delayed because of a rail industry issue (or partners) then the customer can change to another train of the same company to get them to their destination with the least delay.
If are are delayed because you have a separate ticket for a bus or tube service, then you will have to buy a new ticket. Through tickets generally will allow you to take the next available train on an Advance ticket, but it's getting even more complex - so always check. The internal document gives allowable examples, such as Brighton - Zone U12 plus an Advance ticket London Euston - Manchester.
The National Rail internal FAQs for Advance tickets confirm that combination tickets are allowed. The Conditions Of Travel also confirms this in Section 14, though where the train services must stop where your tickets begins/ends
Off-peak & Super-OffPeak tickets:
Having said all that, it does seem slightly unfair that if I didn't have an Advance ticket, but an Offpeak or a Super-Offpeak ticket then I would have to buy a new ticket. I'd ask station staff for permission to travel on the later train
National Rail Advance Tickets:
Minimum Connection Times:
National Rail Guide to tickets: