How about an MG Midget? Can be used in lots of series, very tuneable, good supply of parts.One here:
https://www.racecarsdirect.com/Adver...k3-fia-racecar
Having said that a mate of mine has just bought a very nicely prepared 1380cc Midget for about £6500 so they are about and cheaper than the one I highlighted. Worth contacting the MG owners club race section (or other marque clubs that run race series) to let them know you are looking for a car, they may know what is coming up.
As an aside, if true historic racing isn’t the be all and end all, I would definitely recommend a Caterham. Fantastic fun and the lower powered ones are cheap to run.
I bought my K Series road legal one for less than £10,000 and love racing it in CSCC Magnificent 7s (40 min pit stop races). The Caterham Graduates series and their web site is a good place to look for cars.
https://www.cgrc.uk/forsale.asp
At the end of the season there will be more choice and K Series engined cars should be less than £10k.