It depends how you measure the impact. If you do it by income, there's some truth in that. If you do it by expenditure, it's progressive. If you do it by household income, it's mildly progressive. If you do it in comparison with utility bills, and effect on income, it's very regressive.
Don't forget, it's not a simplistic comparison. The effect of VAT far easier to mitigate than utility bills. We can all cut utility bills to the bone, and the poorest already do, but beyond a certain point, we all need to heat homes and cook. We can't avoid that. But we can avoid the vast bulk of VAT. All you need to do is to concentrate on what you buy in supermarkets. Most foodstuffs are zero-rated, but I wonder how many people have ever noticed the little asterisk, or "V" on some items on their bill? Don't buy items with that, typically 'luxury' items, and your bill's VAT drops.
Of course, as soon as you start buying computers, fancy smartphones, TVs, cars, etc, you start to get clobbered by VAT, and the more you spend, the more you get clobbered. Buy a £50k Mercedes and you'll pay more on that alone than the average family does in several years.
Of course, one exception to that is petrol/diesel. But then, the poorest can't afford cars anyway. Neither rent nor mortgage are subject to VAT, and a fair few other essentials aren't either.
The biggest single factor, though, is that any conventional definition of regressivity relies on a simple comparison of income, not allowing for the fact that the percentage of income that is expenditure drops rapidly as income rises. The so-called regressive effect of VAT relies almost entirely on that, and ignores the effect on the impact of the tax on income levels.
If you load up tax increases on VAT, the bulk of that increase will be paid by the better off simply because their expenditure is much higher, and the proportion of tgat expenditure on VAT-able items, like TVs or £50k Mercedes is far, far higher. The poorest, on the other hand, spend virtually their entire income on essentials, like rent, food, etc, which either have no VAT the first place, or where the effect can be minimised by choosing what to buy or not buy in the supermarket. They can minimise or avoid VAT, but can do very little about green charges loaded onto energy bills.
The wealthier, of course, can impact energy bills. You can thoroughly insulate your home, have argon-filled double or triple glazing, you can run solar panels, ground-source heat pumps, etc. You can even switch to induction hobs, and LED lighting, etc. If you can afford to.
