My house insurance settlement was deducted VAT. How do I claim it back once the repairs are complete? (UK)

Reclaiming VAT from house insurance settlement

I'm in England.

(I posted this in legal advice but didn't get any responses so I'm trying here instead).

I'll try to keep this short and to the point, but if more details are needed I am happy to provide.

We claimed on our home insurance due to an escape of water and were told by the insurance company that they omit the VAT amount and we can reclaim it once the work has been done and we have provided invoices.

The settlement figure was (round figures only) £24k with £4k removed for VAT and £500 reduced for the policy excess meaning we received £19.5k

I have sent them an invoice for £6k for the supply of a kitchen and have been told that I must reclaim all of the VAT in one go by providing invoices of at least the settlement figure (£19.5k). Is this correct, legally speaking? I understand they would prefer to just make one payment, but surely I should be able to claim back part of the VAT amount that was omitted.