Within Scotland, reservations are not necessary. If you're travelling via London, you may want to book the train from London to Scotland. You can do that free of charge via LNER (only their own trains, use “0” as booking reference) or GWR (all bookable British day trains).

As soon as you have your travel dates set you should make your Eurostar reservations. 

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

There's also a night ferry from IJmuiden (close to Amsterdam) to Newcastle.