UK EV charger

I’m wondering if anyone would be able to tell me if I have a looped supply in my property as I’m looking to install an EV charger.

It doesn't look like a looped supply but it is a bit unusual. Your supply appears to be the right hand fuse, the left hand fuse supply goes through the wall (to your neighbours?).
It is probably worth contacting your dno to get them to come round for a visit as it looks as though your neighbour's fuse could be in your property. If this is the case and it is problematic (or potentially problematic) for either you or your neighbour (if this is a supply to your neighbour) then you can give the dno notice to quit and they must make alternative arrangements

For clarity, the issue with a looped supply is that two supplies are connected to a single terminal in the cutout which is rated at 100A. Taking diversity into account this was considered acceptable. However with the advent of EV charging the loads have increased significantly and the 100A rating of the terminal could easily be exceeded. This doesn't appear to be the case in your instance but what can't be ascertained from the picture is whether this is a split phase supply (which it appears to be) or whether there is some (unusual) nternal arrangement within the cutout which means either a terminal rating could be exceeded or the supply cable itself is underrated hence the advice to contact the dno

Quite unusual these days to find an arrangement like this in what appears to be a fairly modern set up.

Normally you would find an unfused link in this side, and the actual suppliers fuse in the neighbours.

Not much protection on the outgoing cores of the cable to next door, if it’s that orange MICC going through the floor.

Looking again the conductor coming from the lh fuse and the lh n appear to be in heat shrink as does the earth. Looks a bit 'home made' as though singles may have been used and the heat shrink is there in an attempt to make the tails double insulated. Doesn't explain the earth though