I agree there! The school usually reflects the local make-up. Where the op is looking, she will have well to do expats around her (I'd say mostly french and americans with a smattering of the rest of the world). She probably won't meet an actually born and bred 'Brit'.
Colour is the least of her worries - I'd look more closely at the 'culture' of the school. Some schools around here seem to have the most awfully behaved children! I mix with them because of school and clubs and the way they speak to/treat their nannies is just dreadful. Horrible snobbishness - then you meet the parents (rude, arrogant, me me me me me, loud, showy)! I'm sure the OP is lovely though!
If you want happy kids, look at St Nicholas next to Hyde Park - not a hard hitter academically (it's strength is in sliding kids back into whatever academic system they have come from) and you won't meet many british kids there. They focus on the kids being happy and confident.
Thomas' (up the road) has a good academic record and a fair boy/girl ratio.
Hill House, I have found american parents think it's too strict. I have found their Admin 'lacking'. It has 'snob value', but probably not as much as it did have when my relies were boys there (Prince Charles went there).
Newtons (over the river, one train stop from Victoria) is relatively new but large and funky.
It depends what you want from the school. If its mainly a colour balance, then you are missing out on an opportunity for your girls to go to some great schools.
My son (mixed heritage), his best mates - Italian, Tunisian, Indian and French all looked extremely similar when they were in nursery/reception (there was a joke that we'd end up taking home the wrong kids). They really all looked the same in their uniforms (especially when caked in mud).
If you live very central, and you will get a very mixed lot of kids.
If you are going to be here long term, you will need to start looking at which secondary you'd like them to go to and consider the 'feeders'.