Dodgy outdoor wiring? Need assistance from RECI certified electrician

Hi,

my neighbours have put lighting in the shed at the bottom of their garden, around 20 feet away from the back of their house and have run the cable through their back wall from their kitchen (I presume branched from a socket), overground and intertwined with our shared wooden fence (photo attached).

On top of that, the cable that they have used looks like internal flex.

Would a RECI certified engineer be able to tell me if that is ok because I have very serious doubts that it is. I would have expected a different flex to be used and the cable to be buried or at least put in some sort of conduit to keep it away from the elements or vermin. The main reason for such a concern is that the neighbours originally had a bar on their decking with the same wiring which subsequently caught fire and I have a very strong suspicion that the flex may have overheated, or become frayed in someway so that a spark ignited the fire.

Thanks.