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It would appear the cab company as registered keeper has been issued a request for the driver of that vehicle and have named you as driver. Were you driving tht taxi at that time? It appears the cab has driven into a pedestrian only area. As we can't see from your photos where the alleged offence occurred we can't offer much help to check for road signs, traffic orders etc.

Show the full picture please, see the sticky above how to post photos on here.

OP, you have driven past two quite clear "Flying Motorbike" signs that mean "No Entry for motorvehicles", and this means taxis as well. Are you new to taxi driving, because these signs are in place all over London, marking the entrances to Low Traffic Neighbourhoods, (LTNs). Whilst "The Knowledge" has to be passed to the Met Police's satisfaction, it doesn't mean you can pass signs like this.

This is just what the hire company has sent me. I’ve requested a fuller photo of the PCN.

OK, fine, but Stamfordman has just posted the video of your cab passing the signs, so the contravention seems made out. If you're looking for a 'technical' appeal, we need all pages of it.

The PCN has nothing to do with you because you're not the keeper.

Unless/until you receive a PCN in your name from the council then you have no liability under road traffic law.

What accompanied the PCN e.g. email, letter etc?

What do Colts Cabs expect you to do, pay it?

You cannot make reps in your name until you receive your PCN.