Yeah, looking at the pictures, Its not so much that its been re-wired in trunking, as there is a load of extra sockets in trunking, you certainly could not follow exactly the same path with the chopping in cables (along skirting), and while in many cases you could go directly horizonal, theres probably a few where you couldn't and it wouldn't be that sensible either unless <1m.
Given that you plan to chase the scokets in anyway, and this is an old cirucit that has been extended from probably very few original sockets, it would make far more sense to just re-wire the cirucits in their entireity. To do otherwise would be having 90% of the work, disruption, mess and cost for a result thats very much inferior, probably limits further alterations, and make already come with issues baked into it.
As has been siad that board is likely at least 40 Years old and the cabling will be too. The existing alterations are pre 17th edition (2008) or have been done later in a non compliant manner. The designation of lift on the additonal board with a test date of 2014, suggests that the property was likely occupied by an older person, and a stairlift was fitted in 2014, and they have now for whatever reason moved out and the lift has been removed, the wiring probably dates from the late 70s and they may have got it re-wired when they moved in, and through the years the sparse provision of sockets which was standard in those days have been supplimented by additions of various quality.