Yes, what HMRC themselves suggest is that you explain to the client what is happening (maybe send them a copy of the confirmation from HMRC saying you have applied to register for VAT), and you initially invoice them at (say) £1200 net with no VAT applied, and they pay you £1200. Once you have received your VAT number, you credit that £1200 invoice in full and issue a replacement invoice for £1000 net plus £200 VAT, which they can then use to claim back the £200 VAT on their next return in the normal way. They don’t owe you anything further at that point.
If they really aren’t prepared to pay the £1200 in full without a VAT invoice then I suppose you could initially invoice them for just £1000 with no VAT on the understanding that you’re going to cancel it and send them an amended invoice for £1000+VAT later, and at that point they’ll need to pay you the remaining £200.
The basic point is that you are not allowed to itemise VAT on an invoice unless and until you have a VAT number.