The aircon unit from a car is something like 6000BTU according to a US website I read recently (so, this would be suitable for cooling a massive car without heat-reflective glass, in a Texas summer). Which means a typical British car is probably only 4000BTU.
The smallest domestic AC units I have seen are 9000BTU.
An automotive unit works on 12V (old ones were powered mechanically though, by a belt, presumably the fan belt). As it draws around 1 bhp IIRC, that would be 50-60 amps. So, you would need to build yourself a very sturdy ac-dc supply. Those would be some pretty sturdy diodes in the rectifier circuit!
To be honest, the cost is prohibitive. A 9000BTU unit can be had for about £130 if you go to Homebase on one of their many sale days.
Also when you say "old car", remember that old cars drove all such items (power steering, air con) off the engine, they weren't electric!
To be honest, you would have more success in adapting an old fridge I reckon. Preferably a commercial one, designed for walk-in fridges. They are designed for mains power supply, all you need is to install the "hot" side outdoors and the "cold" side indoors, with a fan.