If you're a UK resident travelling in Europe, be sure to to get your European Health Insurance Card (EHIC). All UK residents are entitled to coverage under this scheme regardless of nationality, however, those who are not EEA nationals will need to apply by post with supporting documents. Forms are available from the post office.
It is important to note that the EHIC card is NOT a subsitute for travel insurance, you should have BOTH.
The NHS site also provides information about health care in specific EEA countries and non-EEA countries that take part in reciprocal healthcare arrangements.