Cable is sized by how much current it can carry without getting hot. Undersize it and you are not saving money, you are building a fault into the wall.
Lighting circuits use 1.5mm single core. A whole floor of LED lighting draws a few amps, so 1.5mm is generous already.
Socket circuits use 2.5mm. A ring or radial of sockets is protected by a 16A or 20A breaker, and 2.5mm carries that comfortably in conduit.
Cookers and instant showers use 6mm as a minimum, on their own circuit and their own breaker. A 7.5kW shower needs 10mm.
Two practical points. First, length matters: a long run drops voltage, so on a run over about 25 metres go up a size. Second, buy full coils and check the KEBS mark. Cable sold loose off an unmarked drum is often under the stated size, which is exactly the fault you cannot see once the wall is closed.