Was it due to the nature of the domains or them unable to verify your identity? I would think an email to both the registrar and nominet asking for an explanation is the next thing to do. Or if more urgent I'd phone them. Hard for them to ignore you on a phone line.
If it's an ID issue you should be able to easily remedy this with your registrar normally - but you said they had closed your account. I would phone them first as they are the ones responsible for verifying information. They are supposed to respond to your complaints within 5 working days with an explanation/solution. Failing that I would then phone nominet and offer your ID as well as making a complaint about the registrar.
This sounds disgraceful. Once you have moved the domains and gained control of them again you should name the registrar so people are wary of them. If any of the domains resolve to revenue-generating websites I imagine you would have grounds for a claim against them for suspending the domains and causing loss of business and potentially damage to their standing in search engines.
Check the domains in rdap.uk
If they don't have server transfer prohibited or client transfer prohibited status codes then you can use Nominet's transfer service and transfer them to a different registrar. It costs £10+vat for the entire batch of domains.
If the domains have server transfer prohibited, server renew prohibited AND server update prohibited then they are likely scheduled for deletion...