Does UK employment law allow a company to ask for an official audit (or conduct it themselves with their employees) to assure themselves that a union is certified (has 50%+1) to represent the group?
it does....
CAC - Schedule A1 (Part I)
or
Statutory derecognition of a trade union - derecognition ballots | Flexible Support for Business Wales
I know it's Wales, but the law is the same and the Welsh web page is easier to find things in...!