No Starbucks here has free wifi too. And yes you can use your starbucks card to spend / top-up in the UK. Have used mine both to purchase and load in the US, UK, France, HKG and Canada for several years.
You may get a smile when you hand your US card over in the UK - as apparently the UK cards are pretty bland - they grinned when I handed over my Hawaii one.

Actually, it is a pretty good way of getting rid of loose change / spare £$ or whatever as you leave the country if you are not intending going back! Just load the card and spend it later