PS.. The cable supplying the flat is that standard, flat, white
twin-core and earth cable and is 15mm wide, overall. It has insulated
red and black cores (each coe is 6mm thick *including its insulation*.
Is that adequate for supplying the flat, including the said cooker and
shower?

This sounds iffy all-round to me - who owns the property ?

I think this should be looked at by an electrician tbh - sub-mains
should really be in steel wire armoured afaik, and there should be a
switched fused isolator next to the main incomer to the property for
each flat prior to the run of the sub-main to each.

It sounds like these "flats" have been done on the cheap, and I
suspect there are likely to be problems elsewhere, such as the size of
the incoming cable to the property as a whole, before it gets split to
however many "flats" they thought they could get out of it.

It may be a *fire hazard* if you try sticking anything substantial on
the current "installation", which I don't think would actually pass
the wiring regs as they stand.

I've been out of the "hands on" game for about 15 years now, so others
will be better able to advise.