Hi, happylife. I also live in London and agree with scorpio- it will likely be a warm summer here. In fact, it's usually a lot hotter here than most people realise. (ie, it's not always grey and rainy!)
As for clothes, I think a mix of jeans/cardigans/light sweaters for cooler days and evenings is a good idea, along with some dresses/skirts/tanks for the hotter days. Flat, comfy walking shoes are important, too- she will end up doing a lot of walking, as it's the best way to see the city. I wear ballet flats or my gladiators around most days, as do many of the girls in London. A more covered-up shoe or boot would be good for cooler weather, but I don't think a wellie or "winter"-type boot will be necessary.
I also agree that she definitely needs a good umbrella. Make it a lightweight one that can stand being blown inside out a couple times, and that will fold small enough to fit in her purse. I tend to have a preference for brightly coloured ones in the summer, as no one wants to see a sea of black umbrellas in July.
I will warn you/her about overpacking, though. If she is at all into clothes (and comes with a bit of spending money) she'll most likely want to shop a lot, as the fashion here for young people tends to be much more exciting then in North America. When I studied in the UK during my 3rd year of university (I am from Canada, and moved back here after I'd graduated) I bought loads of new things because I was so inspired by all the style around me. So I guess the old adage about packing holds true: take half as many clothes, and twice as much money!
