Whatever you would normally wear,plus stuff for the beach and anything required for specific things (like activities).
That said,I holiday in the UK every year,in August, (Haven and despite what some say it is far from chavvy or slumming it....I even have a full en suite bathroom and walk in wardrobe in my caravan) and take shed loads of clothes because it's nice to feel so relaxed that you feel fab wearing whatever you want!
I tend to take a couple of maxi dresses,couple shorter dresses,leggings,jeans,capris,white linen trousers (fab done the right way!),few (ok,several) tops,couple of tankinis,pair of flip flops,pair of sandals,pair of closed toe shoes for if the weather changes and a pair of more sensible shoes for stuff like long walks,theme/adventure parks,farm parks etc,a couple of cardis (including a light snuggly one for breezes evenings by the sea) and a lightweight waterproof jacket.
Obviously underwear in there aswell,but you get the gist!Just take a few bits for different activities and weather and you're set.