There were 4 generations of the Midget.
The MkI was sold from 1961 to 1964, and it was basically the same car as the Austin Healey Sprite MkII. It had a 948 cc A-Series engine with dual SU carburetors. It made only 46 horsepower, but that was alright in a car of this size, and it was still rather quick and nimble for its era. By 1963, the engine was upgraded to a 1098 cc making 56 horsepower. This was also the first year the car had disc brakes.
The second generation was the MkII, and it was sold from 1964 to 1966. The changes were small, with a slightly bigger engine and some modifications to the door.
The third generation MkIII was made from 1966 to 1974. Output was lifted to 65 horsepower. It used a lot of the engineering used in the Mini Cooper S, although the engine was a detuned version of the engine used in the Mini.
The fourth generation was the Midget 1500, and it was sold from 1974 to 1979. The most apparent change was the new rubber bumpers added in the front and rear to meet with U.S. regulations. A 1493 cc engine from the Triumph Spitfire created a significant boost to power.
These cars are collectible today, and there are hundreds of clubs that celebrate these classic British roadsters. You can probably find one on your area using Google. If you want to buy one of these cars or parts to fix yours up, try using eBay. They also sometimes have project cars for sale. See if you can find a listing from your area.