PS Current best practise does not include putting sockets in skirting boards. But in lots of houses built before mains electricity came along sockets were set into skirting boards on the first wiring because it was easy (no chasing up the wall, just poke your shiny new asbestos covered singles up the gap between floorboards and wall and job done).
On subsequent rewires, people just used the old cable to pull the new cable through so naturally put the socket where the old one was. Not intrinsically dangerous- as long as the circuit design is good and the cables are the right size for the use they're being put to (for power they should be minimum 2.5mm cross section area) then no need to fret.
Getting an EICR (Electrical Installation Condition Report) will be a good idea but that CU doesn't look ancient and the wiring in your Pic 1 looks like PVC so as long as the power rings are actually rings and not spurred to death there shouldn't be too much to worry about. If you're going to redecorate then think very hard about getting extra sockets put in, light switches moved, aerial/comms feeds installed now- you can probably save yourself a fair bit of cash by doing the scutwork for your chosen electrician (chasing walls and lifting floorboards) so all they need to do is run cables, test and connect. Time is money-doing your own chases etc can easily turn a 2 day job into a 1 day or less job