You can't cut the taxes of the poor as much as for the rich, because there's not as much to cut for the former.
I have no idea whether the UK policy is any good or not. But your complaint is a weird one to make.
The situation is more symmetric than you think.
Greater capital mobility cuts both ways: when you lower taxes you can also attract more rich people and their capital.
(I am not saying that this effect will necessarily occur, only that capital mobility comes into play both when raising and when lowering taxes.)
Oh, of course, the real solution to these problems is to tax land and not income nor capital: you can't hide land nor can it leave the country. See https://en.wikipedia.org/wiki/Land_value_tax
Of course, rich people pay more VAT than poor people. In absolute terms.