When people argue about the proportion of taxes paid by the rich, they always base the argument on income tax alone, not on VAT. Proportionately, the poorer pay more of their income as VAT than do the rich.

Here's a nice government document about it.
Office of National Statistics

The proportions of VAT paid by the lowest earners increased over the period of the study, while those of the rich have remained steady. This study is of the Labour period of office. I can't find anything more recent, though there is a prediction here Retail research of the effects of the increase to 20%. (About halfway down.)