And remember: in England is not THAT hot. Imagine moms with young babies in southern spain for example...it gets up to 40 there! I would say just dress her a bit lighter and put her where there is a slight (NOT DIRECT) breeze. As long as weather is less than 26degrees, should be completely fine.
Emily I am originally from Texas, so I KNOW heat! Last time I went home in the summer, my DS was 1 at the time. He came out in the worst heat rash. I felt awful! Wasn't breastfeeding him by then, though, so wasn't sure. Thanks for all replies.