The UK Royal Mail has historically charged a £8 handling fee when collecting VAT and other customs fees on behalf of HMRC. Of course a lot slid through that should have been charged for, because of false value and 'gift' declarations by suppliers, which is one of the factors that led to the loss of the <£15 VAT free import exemption.
I can only suggest that suppliers should consider charging a reasonable handling fee, hopefully a small fraction of £8 for the costs incurred in collecting te VAT on behalf of HMRC. I bet that suppliers will need to hedge against unfavorable exchange rate movements as I strongly suspect HMRC wont settle for less than the VAT in GBP at moment of purchase even if the supplier's native currency has dropped against GBP by the quarterly settlement date, but will quite happily accept any overpayment.
To fix it so the *CUSTOMER* pays the VAT on small imports without a disproportionate handling charge is difficult! Theoretically there could be a government website that let you enter your delivery address and either prepay VAT or enter your (authenticated) VAT number, and generate a one-time valid QR code that you could send to your supplier. On receipt of a parcel with a VAT QR code, customs would scan it, enter the declared value, and either a sticker with 'VAT PAID' or 'Recipient VAT REGISTERED' and the delivery address (so if the supplier attempts to scam HMRC by using a different possibly VAT registered customer's QR code, it doesn't reach the intended recipient), or a sticker with 'VAT of £nn.nn to be collected on delivery, would be printed, which would leave you at the tender mercies of Royal Mail or the courier company's VAT collection fees. However that would require a government competent in commissioning large IT systems on time and within budget, which most governments are bad at, and the British government is historically absolutely incapable of, + considerable initial investment which the current government is absolutely unlikely to do given their anti-China stance.