It looks like your home has been rewired at some point given you have modern PVC cables rather than older rubber. Providing there no faults on the system, which is unlikely providing it was rewired correctly, you could swop the outdated Wylex fusebox and fit a modern 18th edition ay 10 way consumer, which would not only provide full protection to the whole house but, also provide a spare way for an home charge point.
The other option would be to split the meter tail using a Henley block and fit an isolator (needed anyway) and a single way garage type consumer unit to supply a a home charger.
The red and black meter tails going from the meter point to the Wylex fuse box would need upgrading to 25mm, same as the brown and blue going from the DNO Cut Out to the meter point.
The two Earth green/yellow cables seem to be 10mm however a lug would need to be fitted where they connect at the bottom of the DNO cut out rather than just spliced as you see now. The Earth cable going through the back of your fixing board should go unlooped to the gas and then incoming water main. If not an earth block can be used , which would then connect to the gas and then run outside at low ground and come in and connect to your waater main.
The DNO may have to upgrade your cut out to 100A depending whats there already. This would be free of charge for an EV installation.
Other than the coiled up mess below your fusebox, the work looks pretty straight forward upgrade looking at the pictures you have provided. However as mentioned before getting a local electrician to do any upgrade work would be cheaper than having a NON standard istallation done by Motability.
As long as your fusebox is on an outside wall it would be easy to drill through the wall and your looking at a day max for the upgrade work and less for the charger install, One day we will all need the work to be done!
P.s the link you provided is only 4 way and has no RCD. You would need at least a 6way plus 1 for EV charger, it looks like you’d get a 12 or 15 way in the space from you pic’s for a split laod CU.