Overheating

To start with the car would run ok, the temperature would only go up when I was parked for a while, so I changed the radiator fan switch and the thermostat. The problem got worse as soon as I changed them. It would over heat in minutes from cold just sat at idle, and the new thermostat was not opening. So I changed it for a new one and it was the same so I took it out completely and it still was overheating. I then got a hose pipe and flushed the engine and the radiator and it seemed ok no blocks. I then had the water pump changed. The garage said the fan was still not working,
To sum up. Had the thermostat, fan switch and water pump changed flushed the engine and radiator (seems to be ok, no blocks). Car still over heats without the thermostat and the fan still does not kick in unless I bypass the fan switch.