Moving to England on EU passport: NHS?

Hello:

I have been married to a UK citizen for almost 9 years (that's hard to believe:) and we've lived in the US that whole time-- with two trips to London each year so my Londoner hubbie doesn't go too crazy.

My general question concerns the immgration process-- we are seriously thinking of moving to the London area in the next 6-12 months. I was planning on applying for a settlement visa, and saw the prices have gone up to 800 pounds.

Through my father's Cypriot citizenship, I have applied for and will be receiving Cypriot citizenship and passport. This process takes longer than the UK settlement visa but is far less expensive. I understand that with a passport from an EU country, you can live and work anywhere in the EU.

Here's my question-- how does one with an EU passport become eligible for the NHS?

Thanks!!
-Karen