I would advise contacting Unlock about this. You can phone or email them.
While employees have some protection regarding spent convictions, with unspent ones employers can and do let people go if they find out about unspent convictions.
As for "fact-finding mission", I wonder what this means. As a private employer, obviously they have no access to police records and cannot obtain any criminal record info without your consent. Gone are the days when an employer could do a criminal record check directly - now it has to go through the employee.
So their fact-finding will be restricted to Google, asking around your acquaintances/former employer, or asking you to get a basic DBS check. Was your conviction reported in the press?
If your conviction was in the press, they probably Googled you. If not, I wonder how they found out?
Most importantly, I hope you manage to get beyond this, we are all behind you on here, many of us have experienced this. All the best of luck, don't give up.