Insurers do try to find a way to get out of paying a claim if they have concerns. Fraud is the main issue for them, or non-declaration of a material fact - as insurance contracts are contracts of the "utmost good faith".
They can invalidate a claim if you were in breach of the terms in the contract, e.g. you didn't declare something, or they have evidence of fraud. You do need to co-operate with them - this will be a term in the contract that you need to co-operate with them.
You are at their mercy in effect. You cannot speed up their investigation but there is an Insurance Ombudsman to help if they drag this out. You would first have to make a complaint to the insurer first of all.
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. Furthermore, the policy should be “fit for purpose” and “as described”. If it isn’t then you can allege breach of your consumer rights and breach of contract.
You should now make a formal complaint and if that does not resolve the matter ask them for a "deadlock letter", which is a letter giving their final response. Their complaints procedure will be available on their website.
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. They can order the insurer to make a financial award for inconvenience if they have acted poorly or unnecessarily prolonged the investigation.
Once you have the insurer's final response, you can make the complaint to the Ombudsman here : www.financial-ombudsman.org.uk/consumers/how-to-complain
Or by email:***@******.***
Based on the circumstances, assuming the insurer does not uphold your complaint, I am sure the Ombudsman will do. The Ombudsman will look at this case independently and will make a decision based on what happened. Their decision is binding on the insurer. If the Ombudsman did not find in your favour, therefore, you then have the option of suing the insurer for breach of your consumer rights and you have up to 6 years to bring a claim to the court (the limitation period is 6 years from your date of loss, to when you need to issue a claim).