Well, on the one hand--if wealthy overseas parents CAN pay more, maybe they should do. As it might help to control demand levels, which are greatly in excess of the supply of school places that are actually available.
On the other hand, it will increase the tendency of British top public schools to chase wealthy foreign parents, meaning they have no incentive to try and keep their prices at a level that is affordable for local parents, and there is a case for saying that as British public schools are a part of traditional UK culture, local parents who are UK nationals should be prioritized.
Schools which are hoping to hook overseas parents who are prepared to be huge sums for a place are likely to put more money into building glamorous pumped-up facilities, extracurriculars, expensive school trips and other goodies--this will tend to increase the tendency towards fee inflation, putting the schools even further out of the reach of parents who are not extremely wealthy.
On the other hand, the number of people who are educated at these places is so tiny, maybe it does not matter so much in the great scheme of things.
It does, however, make me feel more strongly than ever that these places do NOT deserve charitable status. You wanna run a glammed-up British educational experience for a lot of wealthy overseas elites---well, go ahead and do so. But I don't think you deserve tax breaks for doing so.
One interesting thing to think about is whether as the numbers of wealthy kids-from-overseas grows, the USP of these schoolsthat they provide the ultimate genuine "British" educationwill start to diminish, and that growing numbers could reach a sort of tipping point where the schools start to seem less attractive.