I've just recently signed off a couple of guys on a private cat, group-owned taildragger at a non-licensed field - quite legitimate.
But you do need to supply the aircraft properly insured.
Have you tried Pete Bell and the Chippy (901) at East Midlands?
Atlantique have the C152 at Cov, but quite pricey.
I've also heard rumours that Enstone Flying Club are lining up a Chippy in the near(?) future.