For VAT purposes it's the payment — or the invoice — that fixes it, not the delivery date. The tax point is what decides which VAT return the VAT belongs in, and the basic rule is that it's the earliest of three dates: the date you issue a VAT invoice, the date you receive payment, or the date you deliver the goods or complete the service.
So when a customer pays you a 50% deposit, the tax point for that deposit is the date you receive the money — or the date you invoice for the deposit, if that's earlier. You must account for the VAT on that deposit in the VAT return covering that date; you can't defer it until the piece is delivered. On a £2,000 VAT-inclusive deposit at 20%, that's about £333 of VAT due in that quarter's return.
Each stage payment works the same way: every time money arrives (or you invoice for it), a fresh tax point is created for that amount, and the VAT on it goes in the return for that period. The final balance creates its own tax point when it's paid or invoiced.
One trap to avoid: if you issue a VAT invoice for the full order value when the order is placed, that invoice date becomes the tax point for the whole amount — the full VAT becomes due in that return even though you've only collected the deposit. So don't raise full-value invoices at order stage unless that's what you intend.
Also distinguish genuine advance payments from returnable deposits. A truly refundable deposit (for example on hired goods) doesn't trigger VAT unless you keep it. But a deposit against a future supply — or one you forfeit if the customer walks away — is VAT-able when received, and the VAT stays due even if the customer never takes the goods.
Practically: invoice each payment as it arrives, move 20% of every deposit straight into a separate VAT pot, and reconcile deposits against your VAT returns each quarter. Putting the whole sale through on the order date lands VAT in the wrong period — exactly the kind of mismatch HMRC's systems flag. GOV.UK's guidance on VAT for deposits and advance payments sets this out clearly.