The full rules on this are sadly not in the public domain but the guidance given to rail staff on this issue is pretty comprehensive (extracted from 'The Manual' and copied/pasted from another public forum):
Frequently Asked Questions about travelling with Advance fares.
Q22 - Can a passenger travel on any trains other than the one on which they are reserved, without changing the booking?
A: The following principles apply.
1). Start of the Journey. It is the passenger^s responsibility to turn up at the start of the journey in time for the first train. If they miss it due to problems parking, taxi not turning up etc, they must buy a new ticket;
2). Once the journey has begun. If the passenger is delayed and the rail industry or its partners (as shown below) is at fault, which should be checked with your Control Office, change to another train of the same company is allowed to get them to their destination with the least delay. This is irrespective of combinations of rail tickets held. Examples are:
Included: are passengers travelling on valid:
Through domestic or international tickets, e.g. Brighton- Scarborough route ^TOC▸ X & Connections^;
Through rail & partner tickets for which there is a through bus, tube, ferry or metro fare, e.g. London Zone U12- Leeds, Wisbech Coach-York; Ryde Pier-Hull, etc;
Combination of domestic rail-only tickets, e.g. rail season ticket Skipton-Leeds plus Advance ticket Leeds-Peterborough; or adjoining Advance tickets;
Combination of domestic rail & partner tickets e.g. Brighton- London Zone U12 plus Advance ticket London-Manchester, or Advance ticket Bristol-Paddington plus tube single ticket plus Advance ticket Kings Cross to Hull.
All-Zones Travelcard, PTE▸ -products etc (where rail is included) plus Advance ticket;
Combination of Eurostar tickets into the UK▸ and then either advance purchase tickets from London Terminals or ^London Intnl CIV▸ ^ or ^Lndon Eurostar CIV^.
Not included: for the avoidance of doubt, are:
Non train-company travel on separate tickets e.g. journeys that commence on bus-only, tube-only, ferry-only or metro-only tickets. (This includes ^PlusBus^ which is a local day- Rover bus ticket, not compatible with a medium/ long distance ^Advance^ single journey, so are kept as separate tickets); or
Tickets that cannot be read on-train e.g. smartcards (but allowable where electronically checked, delay verified and Advance ticket endorsed in Travel Centres).