Currently, if you are an EU citizen you may travel anywhere you wish within the EU without hindrance or restrictions. However, you will need a valid passport up until the day that you return in the UK. This is likely to change once we leave the EU when it will be necessary for EU citizens to get approval to travel via the European Travel Information and Authorisation System. Further information can be found here.
The Schengen Agreement signed on the 14 June 1985 is a treaty that led to most of the European countries abolishing their national borders to form the ‘Schengen Area’. You can use the Schengen visa eligibility checker to find out if you need a visa when travelling from the UK to any Schengen member state.