Yes you can, provided that you still have the VAT invoices for those transactions. You can even claim VAT on some pre-registration purchases. Generally:
– services up to six months pre-registration and
– any goods still in stock at the date of registration, that were bought up to four years pre-registration.
See: https://www.gov.uk/hmrc-internal-manuals/vat-input-tax/vit32000 – it’s a bit technical as it’s part of a manual that HMRC produce for their own staff.
Remember that the backdating means you’ll also need to declare VAT on income from that date – “income” being the sales prices, rather than what’s left after Amazon, eBay, etc. deduct their fees.