My ford ka blows out hot air even when the dial is placed on cold(the blue bit)?

This has been happening for the last couple of days also the cigarette lighter stopped working at the same time

The fault with the heater is probably the heater valve, assuming the temperature gauge for the engine is registering correctly.
The 12v socket may be the fuse, or the wiring, or if you mean the actual element isn't getting red hot, it may be dead.
The two faults are unconnected.

Common problem with them is a faulty heater valve. Cheap part, needs to be replaced

Fuse?
Thermostat?