You need to start with taking the Eurostar from London to mainland Europe. If you are travelling this summer you should make the seat reservation ASAP.

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 are also ferrys which might interest you : https://www.seat61.com/trains-and-routes/london-to-paris-by-ferry.htm

Definitely book the Eurostar to Paris well in advance (30€ seat reservation)

Thanks AnnaB

one more question? 
there are rumors of a British rail strike on May 31st and June 3 rd. What do you know about and can we travel if it happens?

thanks again 

Paul

https://www.nationalrail.co.uk/travel-information/industrial-action/

https://www.eurostar.com/uk-en/travel-info/service-information/eurostar-travel-updates

As you can see Eurostar is not affected at the moment as long as you can get to St Pancras. There may though not be any Eurostar availability - check here:

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

@ViejoMochilero Indeed, did you book the Eurostar ? On 31st May availability only to Brussels (6am train) or Lille (6pm train). If you need to travel that day then use a ferry to Normandy and hope that you can get to the harbour by train.

In any case book ASAP