The bank will be registered and authorised by the Financial Conduct Authority (FCA) and you have rights here.
Given the dispute with the bank 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 are covered under the Consumer Rights Act 2015 here which means you have a right to expect a service (from the bank) carried out with reasonable care and skill. Furthermore, the account service 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. Your bank will have details of how to make a complaint on their website if you take a look. You should threaten to report them to the FCA (you can speak to the FCA if you wish, on 0800(###) ###-####.
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 the account and full access restored. They can order the bank 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). This is considered as a last resort though - I am sure the Ombudsman will resolve this given the facts.