Sorry to hear of the issue.
Luckily, there is a quick and easy way to resolve a dispute with your insurer.
Given the dispute with the insurer, you can avail of the Financial Ombudsman Service dispute resolution scheme - which is much quicker than court action and free to use. You have to go through a complaints procedure first.
You wouldn't need a lawyer for this because the Ombudsman scheme is set up for consumers such as yourself. When making the comparing to Domestic & General it just needs to be in simple terms why you are unhappy. They are supposed to provide you with a service after 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.
You can make the complaint here:
https://www.domesticandgeneral.com/content/help-advice-section/faq/cancellations-and-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 in your favour. 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:***@******.***
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. I am sure this will resolve the dispute from having read your question.
The above is the only way forwards short of court action (which is a last resort but an option open to you if the ombudsman does not see it your way).