If the businesses were truly independently owned and operated, it would be allowable. The fact that the arrangement doesn’t avoid any VAT means that HMRC probably aren’t likely to be too worried either. They’re more looking for cases where someone whose business is likely to exceed the £85k registration threshold splits it into two smaller businesses.
But … are you sure this is the best option? There will be costs to operating the extra business, meaning that the VAT registered business will need to charge you more than they are paying for the goods just in order to break even. There ought to be proper contracts set up between the businesses. And the VAT registered business will be required to comply with Making Tax Digital record keeping and return submission requirements from April 2022. Also the fact that the VAT registered business is likely to be filing zero value returns (due to the VAT on income and expenditure being identical) may well prompt an HMRC check, even if they’re then happy with what they find.
You’ve named the company – it wasn’t one that I’d heard of, so I did a Google search to see if others had reported similar issues and found solutions. I’m sure you’ve done your own research, but if not you may want to look at independent review sites…