You should enter the UK as your country of residence (COR). You are limited to 2 travel days in your COR, those are not extra days.
Please note that if you'd like to take the Eurostar, there is a quota for passholders on those trains which can sell out weeks in advance. What would be your travel date and destination ?
Interrail doesn't show availability until you've bought a pass. Have a look here : https://www.b-europe.com/EN/Booking/Pass#TravelWish
If all trains are full, let us know and we'll gladly help. There are a few alternatives like the Harwich - Hoek van Holland daytime or overnight ferry (30% discount), there are also more Eurostar seats to Lille and Brussels for example, etc.
EDIT : availability on Monday 26th June →
- London St. Pancras 09:01 - Lille-Europe 11:26 - Bruxelles-Midi 12:05 30€ seat reservation
- or 19:34 to Lille and Brussels
Nothing to Paris (but you can change in Lille).
Eurostar availability:
London-Paris: 2nd class from 4 July; 1st class from 3 July.
London-Lille: 2nd class 26 June 9:01 and 19:34; 1st class from 27 June.
London-Brussels: 26 June 8:16/9:01/19:34; 1st class from 27 June.
Book ASAP.
The country of residence on your Interrail pass has nothing to do with which passport you use for passport checks. You should use your British passport for your Interrail pass and the you can use your Polish passport for the borders.