Who done the electrical installation? From what I can see, EV aside, I don’t like that the tails are showing single insulation on entry to the Henley block which they should be double insulated until inside the block, and there is a CPC is not sleeved which is not compliant. When did you last have an EICR? I would heavily suggest getting one carried out soon because there, from what I can see, are some things that are easy to rectify but need done for safety.
Why would he need to pay £400-500 to have an EICR done, when an EICR or at least the testing should have been carried out prior to the recent consumer unit change.
Whils’t it can be seen as bad practice, not to terminate with double insulation inside an enclosure, it is pretty common, as a way of identifying live conductors, especially if the electrician does not carry heat shrink, which is quite common with domestic sparks from what I see. The other plausable cause is the sheath has moved when bending the cable. Anyhow, the gap is not sufficient to stick a finger in and at the worse, it would be a code 3 improvement recommended.
The means of earthing is TN-S, I can’t quite make out the connection on the cable sheath however, it use to be in the olden days a soldered (sweated) joint, a variety of what look similar to BS951 clamps, you see on pipes, this was untill constant pressure springs became popular. That makes it very difficult to tell the difference between a genuine DNO connection and one that’s been made inappropriately by bodge and job it electrical! However, from what, I can see of the clamping method for the supplied earth looks original and with TN-S (unlike TNC-S/PME), it forms part of the DNO side and their responsibility, as such it falls out of the scope of BS7671 and is therefore ignored if an adequate ZE is attained and neither did the supplier see the need to esculate for what ever reason. However, if esculated to the DNO, on the grounds of inadequate earthing on a TN-S supply, they install a new clamp if needed, which still seem to be of the 2 part brass clamps and supply a 10 or 16mm tail to whatever MET is available. (they will install a MET block if one is not there) and they will not interfere with a customer’s installation.
I must stress though, the urgency lies, with whatever loose connection (oops!) is causing the burning smell on load. The others are trivial at this point.