OK, here's what I did in the end:
I made the assumption that holiday and sick pay were already included in my hourly rate. So I took the £32.50 agency PAYE rate and worked out what THEY would have paid in employers
NI.
I then, side by side on the spreadsheet, showed what I was paying in employers
NI by going through an umbrella.
They didn't add up, so they've agreed to up my rate and backdate my pay (probably because I mentioned getting the REC involved).
So that's a good result. Next question though:
Why do agencies always want to do things "off the record"? They always promised that they would email a confirmation of our discussion, but none was ever forthcoming.
Something to hide?