Cigarette lighter/12V socket not working

[Panscrank]

I have a 2004 3.2 8p. RHD.

The cigarette lighter port does not work.

I took it out and put a multimeter on it and it reads 0.36v.

Fuse 24 is a red 10 amp fuse on my fusebox, so I tried changing that for a 20 amp fuse and a Headlight level warning came up on the dash. So this led me to think perhaps I got the fuse wrong but all advice online keeps saying 'change fuse 24'

There are three wires on the plug that connects to it; I could only get that multimeter reading connecting as seen in these pics, otherwise it read zero. (This was with the car ignition on)

Any help, greatly appreciated.

[Magnet]

Hello Michael,

Never, ever replace a fuse with a higher rated one. The correct fuse rating has been chosen to protect the circuit. 
Kind regards,

Gareth. 

[cliffcoggin]

I suggest you use your multimeter to test the voltage at the fuse holder and the resistance of the wire between fuse & lighter.