Based on the word cheap I'm guessing under £1,000 so...
Ford Cougar V6 basically a three door Mondeo ST
BMW E46's are dirt cheap at the moment. A good 328i or 325Ci can be £600-1,000
MG ZS190 2.5 KV6 surprisingly quick, just make sure the water pump has been changed regularly.
I would love to say something by Fiat or even Alfa but for under a grand you're looking at 147 2.0ts not the quickest thing out there. 156jts has a paperweight of an engine. Brera 2.2 could be a prospect but for budget expect it to be rubbish. Same for the earlier Alfa GT expensive or expansive.
Quick Fiat for under a grand? Good luck with that one. You might get a Grande Punto 120 but it will have the GM warning lights of death and you may as well save up and get a MiTo 155 (like mine).
Focus ST170 is a nice point to point car but won't set the world on fire. 206gti 180 will be a wreck. Clio 172 or 182 under budget will be thrashed or trashed. 207 1.6 turbo could be good. I have never driven one so can't say.
RX8 if you don't mind two stroke or 12-18mpg from the six port 231. I managed 28mpg from my four port 192 (I prefer the 192 to the 231 but that's a different conversation).
Slim pickings from the 00's. :devil: