Sure you can do that. You can use as many trains as you like.

A Eurail pass seems the best deal for you indeed. Passes get better value, the more travel days or time you have;  (= price per travel day cost decreases quite quickly, the more travel days you have)

You best reserve your seats on Eurostar (train London-Paris, London-Brussels, London-Amsterdam or the other way around) as soon as you can. There are only limited seats available for pass holders. These places can sell out.

On other trains this is less of a problem.

Feel free to come back to us, if you want advice on how to get from A to B, where to reserve, alternative routes avoiding mandatory reservations that are sometimes expensive… Don’t forget the dates and time you want to travel on.

There is a limited number of pass holder seats on the Eurostar between London and mainland Europe. On popular departures and during high season those sell out weeks, and sometimes months in advance.

The best place to see the availability of passholder seats and make reservations on the Eurostar is 

https://www.b-europe.com/EN/Booking/Pass#TravelWish

If you don't get any result, 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