The Mark 2 featured 2.4L, 3.4L, and 3.8L six cylinder XK engines. The US versions featured Solexes which reduced smog emissions along with performance compared to the carburetted models sold in Europe.
The 3.8L engine was very popular with those looking for performance. It could reach a top speed of 125 mph, which was fantastic in 1959, making it a favorite among criminals who need to get away in a hurry.
Police probably hated these cars, as they were constantly having to chase them and they did not have the engine performance to keep up.
There are many dedicated fans to these cars. There are clubs devoted just to this model, and every part can be found through their used parts markets and swap meets, or remade from scratch by manufacturers in Europe and the United States.
If you are looking to buy one of these cars, I'd contact one of the clubs. My second option would be to check eBay listings. Third, I'd check that big Hemming classified catalog.