That is worrying and could be wiring somewhere getting hot/charred or something on a thermostat like fridge or freezer.
Rodent activity tends to produce a hard dead short so that the RCD will not set at all. A slug in a junction box was the most odd one I found causing intermittent faults. They absorb water from the air and become conducting again after a while but soon dry out when powered.
Start at the fuse box and knock off half the circuits. Run the test and if it trips you know that the fault is in the half that are "on".
If it doesn't trip then change the state of all the switches and try again. Then binary chop down halving the number of circuits that are "on" until you have just the faulty circuit.
What you do then depends on if the circuit is ring main or lighting. I wouldn't leave the failing circuit live with the house unattended.
You can binary chop a ringmain fault too but that is perhaps best left to a qualified electrician. Worth unplugging everything and seeing if it is an appliance fault before calling one in though.