If you travelled on a national rail service and left at least the minimum connection time for changes, you’re protected even if you paid contactless.
Delay Repay websites will ask if you used multiple tickets, to which you specify yes then can give details of your contactless payment and the ticket for your onward journey.
Take for example this from GWR:
View attachment 207476
If the ToC that delays your journey doesn’t have a facility to claim for a contactless payment in their delay repay process, you will need to contact their customer service.
Note London Overground and Elizabeth line journeys can form part of delay repay compensation. But if your first delay was caused by them, the industry standard arrangements apply - only 50% at 60 mins.