Reference check taking long

I am using an estate agent to find me tenants. They have found me a tenant who has paid a 1 week holding deposit. I am however very concerned with the lenght of time it is taking. My house has been empty for nearly 7 weeks and I can’t afford to have any further void periods.
The referencing started over 2 weeks ago and I am still waiting. A part of me whats to re-advertise.

They have registered for the zero deposit scheme which is completely new to me. Does anyone on here have any experience how this works? Tenants apparently paid a non refudable week deposit and can claim up to 7 weeks of deposit should there be any damages on the check out. Any advice on this would be great.