liability insurance

Specifically, how would I go about discovering which insurance broker provides the employers liability insurance for A.N.other Company (in the UK)? Is there a public record for things like this, or would I have to speak direct to the company and simply ask?

If there is a record, it would be held at “The UK Companies House” - check out http://www.companieshouse.gov.uk/

The best bet is to ask the company themself.