You need to read the reservation quotes in great detail - they can vary.
As a generalisation, all the main companies in the UK include 3rd party cover (because it is a legal requirement) - but will leave you with an excess which is typically £800 on "normal" cars and upward of £1,000 on "premium" models.
UK companies are much more thorough on damage checks (every scrape matters) than you may be used to in North America....
You shoul get health insurance separately. The NHS will deal with any emergency (and deal with you immediately without any question or financial check) but once you are recovered they are likely to persue you for their costs.