You can buy a roll in / roll out conversion for about £6-7k. Hand them your mini and they hand it back done. Quality varies of course.
Doing it yourself, providing you aren't constrained by time and are skilled with fabrication you could have the whole job done under £1k including the donor car.
The main thing to remember here is that a "medium performance car" weighs in about 1500kg and has circa 200bhp, a mini with an engine conversion weights about 600kg. So your effective power is doubled, very roughly.
The main thing that will affect your fuel economy and performance (aside from your right foot) will be the final drive and gearing. Maybe valvers opt for a diesel gearbox because of the more suitable ratio for dinky small wheels.
Honda engines will run forever and then a bit longer.
20k will get you a rear engine K20 Zcar, space framed and set up with north of 250bhp. It will be an animal, but easily daily drivable... Once you get used to it
Personally, if I was going to drop 20k on a car it would be on something like this:
(If I didn't already have something like this)
Edited by Skortchio, 15 September 2013 - 10:38 AM.