No.
Anyone who paid attention during their school physics lessons ought to be able to total up the wattage of all their appliances, divide by the voltage and then add a safety margin.
Secondly, even if the supply is inadequate, it's not a safety hazard if the current rating of the circuit breakers is set correctly. For example, if I plugged my 13A kettle into his 5A system, it should immediately trip the circuit breaker.
Most power circuits in my UK house have a ring main with cable rated at 20A, so 40A total for the ring. That's protected by a 32A circuit breaker, so we can never exceed the capacity of the circuit.
If it's a spur, the cable capacity is 20A, so a 16A circuit breaker is used.