A RCD plug or adaptor can be active or passive, with the active type it auto switches off with loss of power, I have used them as safety items to stop auto restart with items like angle grinders where the switch can be latched on.
In theory before fitting a RCD we should test the leakage, and this should be no more than 9 mA with a 30 mA RCD, in practice I don't have a clamp-on ammeter I can measure that with, so it has never been tested, so all I have is an insulation tester which uses DC so when putting multi circuits on one RCD it was a suck it and see, with really no idea how close to the wind I am sailing, so I used all RCBO's in this house, that is a MCB and RCD combined to reduce the chances of nuisance tripping, and with a genuine trip reduces how much I loose.
A typical cheap consumer unit costs around £70 and a consumer unit with all RCBO's and SPD cost around £250 for cheapest, so one can understand why people don't use the RCBO option, however there is a middle road called the high integrity consumer unit where you can have a few circuits with RCBO protection. Either for essential services or for circuits likely to have problems.
But looking at what you have reported with no test gear, since over night it would seem connected to lights, so outside lights which have some water in seems the first to look for, since we switch line only, even if switched off, the neutral earth fault can cause tripping.
As to freezer often it is the defrost cycle which causes the problem, there is a small heater often using mineral insulated elements, and if the seals crack, it will draw in moisture, in the main only the line is switched, so an insulation meter between earth and neutral will often show the fault, before we left EU a meter like
this one cost around £25 to £30 but as you can see now jumped to £41 and what you have to consider is it worth doing it DIY or is it cheaper to get an electrician to test for you?
Easy for me, I have the meters already, but multi-meter is useless as uses maybe 9 volt, the insulation tester used 500 volt, most house have 2 RCD's so with freezer best is use a supply from other RCD, however be aware you should not use extension leads with a freezer as the volt drop can result in not starting, so listen to it start and use thickest extension lead you can, if it fails to start don't use extension leads, or it can damage built in overload.
This is a problem with just two RCD's, best practice is to split sockets side to side in a house, as it means lower loop impedance and with failure of one circuit you don't need extension leads up/down stairs, however lights is best split up/down, and the idea is not to have lights on same RCD as sockets for any room, so if some thing trips a socket circuit it does not plunge you into darkness as well, if you get a shock that is bad enough without it also turning off lights, it is clear with just two RCD's you have to split sockets and lights the same way, so if lights split up/down sockets also split up/down, so it means extension leads up/down stairs.
Was it worth the saving with cheaper consumer unit? I used two RCD's in last house and said never again, now all RCBO however if it does trip don't know if earth leakage or overload. However today only trip was clear as to reasons, it was a water leak.
