What does it mean where there is no persons of significant control specified for a company?
It means that in the annual statement of Persons of Significant control, the company stated that there are no relevant parties to declare..
The The Register of People with Significant Control Regulations 2016 defines the criteria for the people (or companies) which should be declared as having control, the full selection criteria is here.
So this company is stating that no single person or other company has 25% or more ownership or voting rights, and that no one has any significant influence or control over the company. This is a rather unusual statement to make for a company.
Our recommendation is to seek reassurances from the company if you are going to do business with them. It may just be an oversight in their annual declarations, however even this indicates that the company might not be as well run as the appear to be.