Don't underestimate how hot it is and do what I did today, traipse around town in wool dress, opaque tights, winter coat (like you say was cold in the morning) with othr shoppesrs wearing what can only be described as beach clothes.
Then get all hot and bothered and had to squander money invest in trousers, top and cardigan to change into. Then, after changing into new clothes in House of Fraser loos, get enticed into spending £30 on make up on the way out!
DON'T wear socks (if trying on dresses nothing more depressing/unflattering than seeing stumpy looking legs with socks on.
Don't take a coat, risk getting cold if the weather turns.
Cardi easier to carry around than coat.