The problem is clearly a neutral earth rather than line earth fault this is hard to find. So options.
1) An electrician would PAT test all items looking for faulty ones but since there is such a variety of combinations causing the trip I personally do not think it is a plug in device causing the problem.
2) An electrician would use an insulation tester on the consumer unit but since does not happen in the day again he could likely not find it.
So if we for the moment assume it is not plugged in and only works at night then two items seem to be what we are looking for.
1) Timer you assure us nothing on timer is causing problem so next.
2) Photo cell.
3) Morning dew.
So looking at picture I see garage I wonder if you have an old outside light with photocell or some damp in garage which the morning dew point is allowing to cause a neutral earth fault?
The writing on the RCD is too small to read but one would expect a single RCD to be pre-2008 and be 100ma designed to protect with a TT supply. I have seen these swapped for 30ma but that is really too low for a whole house. I am out of the trade now and don't know that box but it looks tall enough to take RCBO's maybe some one can confirm if it will or not?
If it has a 100ma RCD fitted then fitting 30ma RCBO's will likely pin point the problem. However looked up your box
The MEMSHIELD 2 MR30 30MA 10KA POD which turns the MCB's into RCBO's costs £99.99 each clearly it would be cheaper to renew whole consumer unit than to fit RCBO's in that one. Looked at
Screwfix and RCBO's at £22 to give some idea of the problem with MEN prices.
Of course changing consumer unit you can have split system with two RCD's or combination of Main switch RCD and RCBO.
The Eaton Memshield3 Rcbo is cheaper at around £46 even they are expensive maybe some of the others on here recognise the board and can advise more.