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Turning to the question, the issue is at their end and you were right to complain.
You are covered under the Consumer Rights Act 2015 here which means you have a right to expect a service (from the insurer) carried out with reasonable care and skill.
If the complaint does not resolve the matter ask them for a "deadlock letter", which is a letter giving their final response.
Once you have the deadlock letter the next step would be to escalate this to the Ombudsman - they will investigate and liaise with the insurer which would hopefully result in a reinstatement of cover under the policy/an acceptance of your claim. They can order the insurer to make a financial award for inconvenience if they have acted badly (which they have in my view).
You can make the complaint here : https://www.financial-ombudsman.org.uk/consumers/how-to-complain
Based on the circumstances, assuming the insurer does not uphold your complaint, I am sure the Ombudsman will do. I say this because their adjuster which was dismissed from employment binds the insurer to any agreement - under vicarious liability.
I hope this helps - if you can please accept the answer and give me a 5 star rating (there should be a button at the top of your screen to do this), I can answer follow up Q&A's at no extra charge and Just Answer will credit me for helping you today.