There is a reciprocal healthcare agreement in place between the UK and Finland, which guarantees free provision of basic emergency treatment on production of a valid E111 form (available from post offices).
E111 is not a substitute for travel insurance, and you should still take out a comprehensive policy prior to travel in case you need to be evacuated back to the UK in an emergency. The hospitals in Finland are of a similar standard to the UK, although with state hospitals there can be delays in treatment. Travel Insurance will include private medical care.
You do not need any inoculations to visit Finland.