Unless they are 60+ years old and rubber insulated, the existing wiring is very likely suitable for continued use.. I assume they won't need to replace all the wires in the house. I
The consumer unit should be replaced - it has a single RCD for all of the sockets which is very far from desirable, adding even more to that will not comply with BS7671, and the RCD is of a type which is not permitted for new circuits.
No RCD for the lighting or other circuits. No surge protection either.
Replace with new consumer unit and RCBOs for all circuits. All existing circuits would need to be inspected and tested, some repairs/alterations might be required.
There is no issue with loading, but having everything on a single RCD is a problem, as many modern electronic items have a certain amount of leakage current by design, and a whole pile of those on a single RCD will result in tripping even when there is no fault.
The other problem is that you don't want every socket in the house going off and disrupting internet, office items and whatever else just because the kettle leaked.
As for the circuits, assuming existing wiring can be used:
upstairs 32A ring (red) cut in half and converted to 2x radials, add additional sockets to those as required.
downstairs (green) ring the same - convert to 2x radials and distribute the new and old sockets on those.
kitchen - retain existing ring, add socket(s) to that if needed.
Whether the boiler is with the kitchen sockets or not changes nothing. As it's already with those then keep it like that unless you want to make a pile of extra work.
Old water heater / immersion not used, but the cable should be left in place for possible future uses.
Cooker circuit and lighting circuits unchanged.

