Department HR Reference Nightmare - Any Advice?

I'm having a bit of a nightmare trying to get a reference from SSCL for a new job with a start date of next week. Can anyone help?

I worked at Defra for four years and left in 2020. Since then, I've had a couple of different jobs. I'm now due to start my new role, have left my current job, but am not able to start until Defra HR (SSCL) can confirm my period of working for them (apparently a personal/manager reference is not enough).

Every time I call SSCL, they say they don't have a record of me even though I was at Defra for four years. Has anyone else had this experience?? How did you solve it?

Am worried that an SSCL 'computer says no' error is going to lose me my job