In terms of what your insurance covers - you have to slog through the small print and read exactly what your policy / policies will cover.
The vehicle will have (what we call) third party cover (legal requirement) provided by Avis but you are likely to be on the hook for an excess (deductible) of £1,000 to £5,000.
If your cover does operate in the UK, note that no rental company will recognise it. Rental companies in Europe never deal with credit card or other third party insurers. That doesn't mean you aren't covered. What it means is that if you suffer damage (no matter who is at fault) the rental company will charge your card and is down to you to reclaim money that from your insurer.
Expectation management. All rental companies in Europe are strict on damage control - strict in a way that shocks some north American customers. Your vehicle will come with an existing damage sheet - make sure you check that carefully against the vehicle before you drive away from the rental depot.