If you still want to travel and the train gets cancelled, you're entitled to overnight accommodation in London so you can continue tomorrow. They might allow you to stay overnight on the train in the platform; Caledonian Sleeper sometimes do this, but since the Night Riviera has to come empty all the way from Reading, I don't think GWR tend to do it. So GWR would probably have to arrange a hotel for you. You can also claim Delay Repay based on your arrival time - likely 100% compensation as it would be 2+ hours later.
If you instead want to abandon the journey completely, you'd be entitled to return home (to Lichfield?) and claim a full refund of all the tickets you bought for the journey. This would be claimed from the retailer you used to buy the ticket(s). But that presupposes that you had a valid cross-London connection - this would require that you allowed the minimum connection time (MCT) when crossing London, bearing in mind this is longer in the late evening, and that one (or both) of your tickets covered the Underground transfer.
If you had tickets that were to and from London Terminals, and were planning to use Oyster/contactless on the Tube, it is unclear that would legally speaking amount to a through journey since the NRCoT requires that:
the train services you use Call at the station(s) where you change from one Ticket to another
Notably, Oyster/contactless PAYG arguably only counts as a Ticket if it used on National Rail services:
“Ticket” means any physical or electronic document or record which entitles a passenger to make a journey on the National Rail Network
Anyway, you can cross that bridge if it comes to it.
