The NICEIC have said that it looks like I have a Mode 1 charging point.
They are wrong. The charging mode refers to the whole system of power supply, connector, cable and vehicle. Not just the wall socket.
Mode 1 was where a car connected to a 13A or 16A socket outlet using just a normal cable. Rarely used even when it was a thing and certainly not applicable to any modern electric vehicle. Due to the total lack of safety devices, it isn't recommended for use anywhere ever.
Mode 2 is connecting to a the same 13A (possibly 16A) socket outlet using the charging cable for the vehicle, which includes a control box within the cable itself, that box containing various safety devices. It's the cable supplied with the car and usually referred to as a 'granny lead'.
They are intended for short term, temporary use where there is no other option available.
Mode 3 is what most people have installed at their home - dedicated charging equipment with the charge cable either attached to the wall box, or in some cases removeable. The safety devices are usually built into the charge equipment, or in some cases separately, but either way it's all provided in the installed equipment, the cable that connects to the vehicle is just a cable with the appropriate connector on each end. Also installed at many car parks, supermarkets and similar.
Mode 4 is only available at places such as motorway service stations, some car dealers and other places where it's necessary to add a very substantial charge very quickly. Uses high current DC directly into the vehicle. It's the one that can charge 20%-80% in about 20 minutes or so.
What you have got could be used for Mode 2 charging, but as I replied previously, that socket outlet needs to be removed and replaced with proper charging equipment.
The socket is just there because something needed to be put at the end of the cable and a socket outlet was the easiest and cheapest thing.