Will you be visiting during warm weather? I was traveling all over Europe for 3 weeks and brought 2 pairs of jeans (washed them I think only once or twice) and I also brought about 4 skirts, all very lightweight, two dressy and two casual. I don't wear skirts a lot at home, but they were great for my trip because they were lightweight and thin.
I also brought several different cotton tank tops I could mix with all the bottoms, and I brought a very versatile white cotton pullover shirt with a hood to wear when it was chilly. Also, I fell in love with scarves while in Europe as I think you mentioned you would bring. I bought 3 in Paris and used them as wraps, knotted around my neck, and also as a blanket while traveling by bus!
I did bring a pair of sneakers, but ended up wearing flip flops the majority of the time, even though we did a lot of walking. If I had to pack again I'd bring all the same stuff, minus the sneakers and one pair of jeans, and plus a pair of ballet flats. Keep in mind that even in June, it got chilly at times, especially in London!