Your question as hard to answer like this. Best provide more details: when are you travelling? Which trains are you looking at (train number, departure time,...) ?

Educated guess for an answer:

On a travel day, you can take as much trains as you want. As a UK resident, taking a train in the UK to London will trigger an inbound/outbound journey (as you only have the right to travel two days in your own country with a pass) .

If you take your Eurostar later that day, no problem to do that. You need a reservation for Eurostar (mandatory), best get these as soon as possible. If you spend e.g. the night in London, it's best to buy your journey from Home to London as an advance ticket, taking Eurostar From/into the UK wil also trigger an inbound/outbound journey. 

Other UK trains (long distance intercity services) only have optional and free reservations, recommended to make one during peak times, otherwise you're good with just registering the train in the rail planner app and generate the QR code. Making reservations is very dependent on route and train company though. 

The pass is your ticket, you won't need reservations for the most trains in Europe (except for the popular, cross-border high-speed trains).

Check here: https://www.seat61.com/interrail-and-eurail-reservations.htm

If unclear, feel free to ask questions

The app doesn't book anything, you just need to register the trains you take; it's the digital equivalent of writing a train on the trip report of a paper pass. There's no real need to do that until you're about to board a train.

If you don't need a reservation, then your pass is all you need to travel. For a mobile pass, the QR code, together with the train(s) listed below it, constitutes a valid ticket.

In GB, you can still make a reservation free of charge at a ticket office or online via LNER (their own trains) or GWR (all reservable trains). The rail planner app is incorrect that a reservation would cost €6.

So this is really helpful. And our train in the UK (home to London) would immediately precede the Eurostar from London to Amsterdam (already booked). The responses do raise another question though as you state that tickets can still be booked via LNER for example.  Does that mean that can use an Inter-rail passcode of some description to book seats on trains directly on their websites? Case in point - I’m trying to book a sleeper (Amsterdam to Innsbruck) - booking shows on the Night Jet website but I don’t appear to be able to get the same options on the planner … can I book direct on the NJ site and transact a discount with our passes? 

Indeed, and it won't use another in/outbound day if it's on the same date.

Not tickets but reservations. Your pass is your ticket.

You can use "0” for reservations via the LNER website (as their help says). But each website has its own procedure. Often however, for optional reservations, you only need to choose a "seat only” option or something similar.

Sure, you can book reservations anywhere you like. For Nightjet, nightjet.com is usually the best way. Add the Interrail/Eurail discount for all passengers. For other trains, check this web page:

https://www.seat61.com/interrail-and-eurail-reservations.htm

Okay. Sorry - what is the Interail / Eurail discount? Is that my pass number or is it something I simply select which applies a discount which is then only valid when I present it with our passes? 

Yes you select the discount and that's it. The discounted price will appear and onboard you'll need to show both the Rail Planner app (pass/ticket) and the reservations PDF.

Please use nightjet.com as the overview is clearer and there's no booking fee.

Btw night trains are best booked ASAP as they're popular and Nightjet now uses dynamic pricing even for passholder reservations.