Which is the pozitife point centre or edge?

The cigarette lighter/power outlets on a 2010 Ford Focus are referred to as, "power points." The are two power points on this vehicle, designated as power point 1 and power point 2. Power point 1 is powered by fuse #15 (20A) while power point 1 is powered by fuse #3 (20A), both of which are located in the battery junction box at the left rear of the engine compartment. You can read more about how to handle cigarette lighters that don't work here: https://www.yourmechanic.com/question/the-cigarette-lighter-is-not-working-what-should-i-do-by-isaac-z

If the cigarette lighter has been in use for cigarettes ... it could be that the contacts within lighter outlet contact points are heat damaged and connection to auxiliary device may not be made electrically ... You could test if you had a voltmeter ... but if you can visibly see heat damage... perhaps you could try scratching any obvious tarnished metal contact point with screw driver... . (the central contact point is the one that is likely to be tarnished requiring cleaning) unless it is a loose electrical conection gone bad... but that would require removing the cigarette lighter.
Note: recommend to remove the cigarette lighter fuse before attempting to insert a metal object into the cigarette lighter... else sparks may fly and the fuse will/or should blow.

good luck.

The harness end is there taped to the main dash harness somewhere under the dash near the power points.

I don't see a power connection to the three components. The interior lights are on a 20 amp courtesy fuse, the cig lighter should be on a 30 amp ACC fuse, and the mirrors are probably powered thru the key on a different 30 amp ACC fuse.
The only common factor would be a ground connector somewhere.
If they all died at the same time, a ground problem would be my guess.

looks like a cigarette lighter port,made for power for accesories,
they don't want to call it a cigaterre lighter anymore.Usually the power point has a lesser amp rating than a lighter port.

the cigarette lighter fuse is usually the accessories fuse, the ignition switch may need lubricating, to do this use graphite powder put some on the edge of the key as you push it into the switch, you may have to do this a few times to get enough in,DON'T use WD40 or the like as this only attracts dust & clogs the switch up more.......hope this helps......cheers.

As they don't make one you have 2 options.

1) Buy another Mains Adapter and Cigarette Lighter Plug, Cut the Cable & Connect to the BMR100 and connect it to the Cigarette Lighter Plug.

2) Buy a small (100W) 12V to 240V Inverter and plug your existing Mains Adapter into this. You'll get one from eBay for about £10.00 to £15.00.

For 2006 VW Jetta 2.5, cigarette lighter fuse 20A (yellow) is placed in the fuse box on passenger's side. See picture below:

I would go to your nearest Radio Shack or Walmart. They have a plug that has different ends to match your unit. Please let me know if this helps you.