Given the dispute with the insurer(s), there is an Ombudsman scheme which is required before you taken an insurer to court. The reason being, the Ombudsman scheme is free to use, quicker than court action and legally binding if you accept the Ombudsman's decision.
If you sued now, you would be asked by a judge why you chose to involve the court - if you have no answer to that the judge could dismiss your claim and order costs in favour of the insurers, so it is a risk to do this in my view.
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. The insurer will have a website with details of how to make the complaint - it should show up on a Google search if you type in the insurer's name followed by "complaints".
When you do make the complaint, tell the insurer you plan to report them to the Financial Conduct Authority (FCA) who regulates them. You can reach the FCA to report them on 0800(###) ###-####if you wish. It may speed matters up.
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 resolution. They can order the insurer to make a financial award for inconvenience if they have acted poorly.
Once you have their final response, you can make the complaint to the Ombudsman here : www.financial-ombudsman.org.uk/consumers/how-to-complain
Or by email:***@******.***
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). You could do it online via the http://www.moneyclaim.gov.uk website. You can claim for your loss and also a litigant in person rate of £19 per hour under the Civil Procedure Rules.
As I mentioned above, this is considered as a last resort though - I am sure the Ombudsman will resolve this given the facts.