You may be able to get your insurer to reconsider but it depends on your insurer and how the post-accident audits are conducted. If you are very unhappy with the car valuation your insurer has given you, that makes your car a Cat S or N write-off even if repairs are not too costly, you can present evidence of higher valuations.
Use Motorway’s Car Value Tracker for a free, instant valuation to challenge your insurer. You can also use any valuations made by dealers, in writing, and also check your car finance agreement for any Guaranteed Minimum Future Value or other valuation information.