I don't think you'll be able to persuade them to change their valuation. I think they use reference data, based on trade values, that they have to adhere to.
Like I said earlier (
here), same thing happened to me. It should be possible to get them to agree to give you a cash payout instead. In which case you would get to keep the car (without any recorded write-off against it) and the £2.5K that they would've paid you to replace it, though they may offer less as a cash payout, or deduct the scrap value. You're then free to take the car anywhere you like for the repair and have it repaired with used parts if you prefer.
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Mark
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2002 FE S8 Ebony Black Pearl
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Cars Owned:
The Tesla Era: 2020 Model S Performance Ludicrous+ (present)
(Black, with all black premium interior and carbon fibre décor, 21" sonic carbon twin turbine wheels and FSD capability)
The Audi Era: '97 A8 4.2 (Ming Blue) --> '96 A8 4.2 QS (Dark Green) --> '02 FE S8 (present)
The Citroen Era: '84 BX 1.6 RS --> '89 BX 1.9 DTR Turbo --> '94 XM 2.0L Turbo --> '96 XM 2.0L Turbo Exclusive --> '00 Xantia Activa 2.0L Turbo
The Banger Era: '76 1.2L Lada VAZ-2101 (Ruski Fiat 124) --> '80 1.7L Morris Ital HL, finished in Ermine White and Rust