Your E111 is no good in Bulgaria. We had 7 days in Bourgas hospital last year and they told us because they are not in EC it doesn't apply. Make sure you get good insurance before you go.
I got an E111 AND Travel Insurance, best to be over-covered than under-covered.
Ski insurance is available from £20 if you buy online. Our local Insurance Broker quoted £31.60 over the counter, Post Office was £40 and Thomas Cook was £47!
Cover over the 'net was as good if not better than over-the-counter versions and cost considerably less.
E1-11 is valid but only with your NHS card also. the EU thing is totaly nothing to do with it, i have students from all over the world, carrying several equivelents, from around 40 countries, all of which we are covered by e1-11 in. I also travell a fair bit and although its valid, its only a few countries that automatically accept it, some will try to fob you off, or just dont know. If you want the country list email me ill scan and send it too you.