Seat reservations are not mandatory in the UK, except on night trains.
If you want to book a reservation, you can do it free of charge via GWR, see this overview:
https://www.seat61.com/interrail-and-eurail-reservations.htm
No reservations possible for London to Cambridge.
For Cambridge to Edinburgh, I’d consider reserving the LNER part of the journey, which will probably be from Peterborough I guess - especially if it’s a busy time of day. Use the link that @rvdborgt gave to see how to do online, or just do it at a station - always free.
But it’s not really necessary. I’ve always been able to find a seat, even without reservations.
Actually, the link above works for all UK operators. But for LNER specifically, you can also do it on their own website, which is slightly easier - and you can choose your own seat.
Just enter 0 when it asks for a ticket number.
https://www.lner.co.uk/travel-information/make-a-reservation/