My understanding as far as museums are concerned is that it includes:
1. Holders of a EU passport even if they may not be resident in the EU
2. Non-EU passport holders who can demonstrate their residence in the EU - usually by way of an identity card. However, unlike many EU countries the UK does not issue identity cards so I am not sure what could be acceptable as an alternative - a UK driving licence?
3. Non-EU students in full time education which would be evidenced by their student card.