E111 is out of date, you need an EHIC card, you can apply on line. As scotman says, they have a health service, but I know that all GPs are private, I am not sure about any reciprocal arrangements with the UK health services.
The interesting thing is, the Channel Islands are not part of the EU and as EHIC is for use in EU countries, I presume it`s not valid there (unless anything has changed recently)
Also, if needing a new or replacement EHIC, make sure you use a .gov type website because they are free. I notice several very official looking sites that charge for them.
Just remembered that our old EHIC (Health) card expired last November. I know you can renew it online but will I have any problems given that it has actually expired and not just to carry on renewing it.
Ann:
The system doesn't differentiate between a renewal and issuing a new card. You still have to enter the same details. So it's completely irrelevant as to whether your old card has expired or not. (My own preference would be to phone up. I think that it's much simpler and quicker: 0845 606 2030).