I'd use a small-block Ford; believe it or not, an H.O. 302 is actually weighs less ,with alloy heads, than the BMC engine. It should fit with little (if any) cutting of the unit body. The hood clearance may be a problem. The stock rear axel will hold up if you keep near stock tires and engine. You should be able to find a shop locally that can narrow a Ford axel if you want to go faster. My dad had an A with a 305 hp 289, automatic, and Ford axel. It pulled mid 11s on the little skinny stock tires. The mpg stayed about 20-25. With a later 225 hp EFI 302 you should expect more mpg. Remeber that you'll be lighter so it'll actually take less power to roll down the road at X speed, you'll just have more power on tap. A Mustang GT driven lightly can get between 25 and 30 mpg so I don't see why the MG would be worse with 600-1000 lbs in weight savings.
A small block GM will also work but you'll have problems with distributor/fire wall interference resulting in the need to cut some sheet metal out. The GM is also heavier. Even with the Ford you'll need to notch the front crossmember. If you want a 2.0 turbo the Toyota 3S-GTE is a tougher engine than the SR20DET. Both are available in RWD configurations. The 302 is tough to beat though, with turbo options up to 1,700 bhp! (not for the stock MG unit body)
Also, a turbo BMC engine should be able to make 180-200 bhp and would be very unique and in my opinion, very classy.