There is no way to get from the UK to mainland UK without reservations. The only train connection is the Eurostar with a limited number of pass holder seats on each departure. The cost for a 2nd class reservation, one way, on the Eurostar is about 30 EUR.
As there is a limited number of pass holder seats on the Eurostar and on popular departures and during high season those sell out weeks, and sometimes months in advance, it is important to make the reservations ASAP.
The best place to see the availability of passholder seats on the Eurostar is
https://www.b-europe.com/EN/Booking/Pass#TravelWish
Press "later trains" and eventually you will find the next available connection.
If you have a mobile pass you need to generate a Pass Cover Number in order to make the reservation at b-europe. You do that here in the PCN generator:
https://community.eurail.com/news-and-announcements-39/pass-cover-number-generator-is-live-5653