Hi,
I'm not in the same boat but for a while it looked like I would be. I wasn't sure my ex employers would agree to give me a reference. They did in the end.
What my agent told me was it isn't ideal, but it's not the end of the world. I would have to write the stat declaration in as much detail as possible and then back it up with other evidence, like payslips, tax records showing you were in the company's employ, etc. A technical interview would be required too. That's all I can remember for now, but you should probably consult a professional before doing anything.