Some of the earth sleeving is green, implying it was done before around 1977, some if it green/yellow, though unlikely a lot of work done after.
Certainly there are a lot of good reasons for changing the board to a modern one, ideally an all-RCBO style (so each circuit has a combined MCB for over-current protection and an RCD for earth leakage protection):
- Any after 17th regs amendment 3 are metal to be fire-resistant
- An 18th edition board would have surge protection
- Anything in the last decade or so would have additional RCD protection against shock
While the cables are old they are PVC (not the horrible old VIR rubber) so if they are in good condition (insulation resitance high, no signs of thermal stress or rodent damage, etc) you can probably use them for decades more to come, and that reduces the decorating impact of an update.
However, it would be worth considering having all of the accessories like 13A sockets and light switches updated if they are getting on and any have switches that are a bit sticky in action or cracked, etc. Maybe not essential if they are still usable, but then it would all be tested as part of the board replacement as well.