This is a post of limited interest to anyone who does not own an R53 Mini, but I couldn’t find a simple answer anywhere else on the Internet, so here it is anyway.
As a proud first-generation modern Mini owner, the question of how to do better than 20mpg in my almost exclusively city driving routine weighed heavily on my mind, until I decided to test it. Some cars (such as my mom’s old BMW 318i) do best at higher revs than you might expect. The Mini does not. What you want to do is short shift as much as possible, with a target cruise RPM of 2000-2500. My suspicion is that, whenever the supercharger bypass valve closes at ~3,000 RPM, you get such a large amount of added air that any economy you gain from being nearer the middle of the power band is wiped out by the necessity of adding so much more fuel to get the mixture right. I went from 20mpg to 24mpg when I tweaked my driving.
7/14/2015 addendum: I’m back to highway driving, and I find that the same axiom still holds. Short shift—I went from about 275 miles before the low-fuel light comes on, to well over 300.