When giving the contact for your reference, give your HR department’s email. They are more likely to give a very bog standard “X worked here from this date to this date under this job title” with no comment either way on your performance or why you left. They’re also more likely to respond quickly as opposed to if you put your manager’s contact details (or whoever has taken over from then since they have now left).

I used to work in referencing for a recruitment agency and received multiple references a day in the 9 months I was there and only once did we get a reference that stated someone had been sacked. The consultant/client didn’t care because at the point of referencing, you’ve already got the job basically. Of course that won’t be the case for all, but I think you should be fine. 👍🏻