and when nothing has just been switched on.
are you 100% sure? What about things that have been switched on for some time? If it is a genuine ring circuit it will usually be have a 30A or 32A fuse or MCB. Has it?
A 30A circuit will run two 3kW loads indefinitely. However if you also have some other appliance such as a washer, drier, dishwasher or oven on the same circuit at the same time it will be overloaded. A kettle or toaster can do it, but is often not on for long enough.
unplug appliances that are not in use
Examine plugs for signs of scorching e.g. from loose wires inside
If not a faulty appliance, it may be damaged cable.
Common suspects are:
nail or screw into wall or floor has hit a cable (this can be very dangerous)
cables under floor nibbled by rodents
water getting into something, e,g, rain into a garden socket or a leak into a connection under sink/behind washing machine
cable under appliance e.g. washing machine has been crushed when appliance pushed back into position
It can also be a socket that has been damaged by overheating, e.g. two large appliances such as washer and drier in a double socket