Congratulations on you getting the MOT, not an easy accomplishment in the UK.
Did the water tank spit out water or did it read high on the temp gauge?
The water pump is driven off the engine pulley with a belt that also drives the alternator. If your battery was charging / amp meter reading or alternator lamp not on, your belt is most likely installed and running. Water pumps generally leak when they fail, they normally don't stop moving water.
The thermostat being stuck closed is the most common reason for over heating. The 351c thermostat is unique to this engine and if the incorrect one is used, it can also cause overheating. Have a look at George's post in this link which have pictures..
http://pantera.infopop.cc/eve/...50045562/m/346105744A stuck thermostat will cause overheating pretty quickly. Remove the engine cover over the air filter, remove the air filter and you should be able to see / touch the engine water outlet pipe and see where it connects to the water tank. Start the car and let it idle, watch the water temp gauge (hopefully the water temp sensor is located in the engine block right next to where the water outlet pipe bolts to the engine, which holds the thermostat). After a couple of minutes if you are touching the water pipe you will feel it get a little warmer. When the water temp gauge starts to get near half way, the water pipe will or should suddenly get very warm as the thermostat opens. You can use an IR heat gun if you have one, your gauge may read lower when the thermostat opens. Don't let the car over heat.
In the link above is a diagram of the water flow, only the system tank has a pressure cap.
Or you can look at JFB's post who beat me to it..