Ford KA water heater problem

Common fault on this car/
1 when did it start to happen,
2 was there antifreeze in the coolant,
3 where is the coolant leaking from,

The most likely cause if there was no (or little) antifreeze in the coolant is that your engine has frozen up, and upon starting you have sheared the impeller on the water pump, you will need a new pump.

If the problem has been around lomger than the current cold spell,it could be the Heater control valve fitted to the bulkhead, these disintergrate and allow pieces of itself to journey around the system normally ending up in the thermostat housing amd jamming it shut, or the thermostat housing itself could have failed.

It could of course be the thermostat itself that has failed, if you are SURE that the engine has NOT frozen start by removing the thermostat, check the housings integrity, and the operation of the unit by pouring boiling water on the stat and seeing if it opens.
Hope you get it sorted soon.

most likely problem will be your head gasket has gone but before to rule this out have it checked by a garage with a device called a sniffer that changes colour and tells you if your head gasket has gone rather than replacing a load of parts that could be and in the long run save you money

A pressure test on cooling system should show any external leaks and a sniff test (block test ) will check head / gasket .Once cause of leak has been found and repaired , thermostat needs checking and correct amount of antifreeze added .