"PES" means "Public Electricity Supplier" - the company who sends your electricity bill - they are the people to contact if you want an upgraded earth. There are various other companies involved - and Scotland is not the same as England - it may be a different company that looks after your meter, or the wires in the street ("DNO"=Distribution Network Operator) but you aren't required to know who they are and contact them yourself, your PES is responsible for dealing with you and passing on requests to the other contractors.
"TNC" is a kind of earthing arangement, and that little terminal you show does look to me like it is the supplier's earth, so I think you should join all your earth wires onto that, via a Block like I illustrated. The terminal you have is smaller than I am used to on modern installations in this area, and it looks as if someone has unsuccessfully attempted to put three wires into it. One 16mm wire, fully inserted, gripped by both screws, and going to a block where all the others can be fitted, is the better way to do it.
If you get a local electrician in, he willl be familiar with the arrangements in your area and can do it for you, or advise if an upgrade is required.