I am happy to recommend the Tudor Dairies in Henley-in-Aden.
More commonly known as 'that tea room with the ice cream'
Good menu, including whopping toasted teacakes & cream teas as well as savoury stuff (breakfasts served till 1400, IIRC), and, of course, about a gazillion flavours of ice cream.
Oh - and forget silly closing times - they're open till 1730 on a sunday!
Tea was good - and they have a big photo of a club outing on their wall.
Staff were a clueless but pretty charming bunch of teenagers, but all was well.