Check the rental T&Cs. Liability (3rd party) insurance is mandatory in the UK, and so may be included in the rates. However, some companies and booking sites allow customers from North America to book rentals without this insurance, but it's pretty inconsistent. If you don't have any such insurance, you'll be driving illegally.
As for medical, I'm not aware of any UK car hire companies that cover this, as we're covered by the NHS (although you do have to pay a contributory fee for motor accidents). However, I'm a local, so wouldn't be aware of such schemes anyway