All the consumer unit shows is the labels have not been updated so you really have not a clue what trip does what. The problem with British consumer units is a MCB does not switch the neutral, so you don't have a clue which circuit is causing the problem, however a good start would be to work out what MCB does what and relabel so once an electrician does call he will know what he is working on.
In theory when installing a RCD one should test the back ground leakage, all AC circuits leak some current, and the idea with a 30 mA RCD is to keep this below 9 mA and since the RCD trips between 15 and 30 mA it should in normal circumstances not trip, however when the installer could not even be bothered to correct the labels there is little chance they measured the leakage, so it could well be right on the edge.
In theory it should only trip with an imbalance, however I know my old house electric storms could take it out, and I would get a run of trips, then it would hold in for a couple of years, I would assume spikes on the line, and having had RCD protection for some 30 years I know there was no real fault, I had simply put too many circuits on one RCD, I have 4 circuits on each, this house has a RCD per circuit, using RCBO's which is a RCD and MCB combined, as I learnt my lesson using multi circuits on one RCD.
There are two methods of fault finding, one is have a guess at likely problem can check it, the other is to methodically work ones way through the system, in practice we use a bit of both, so yes you can remove covers looking for spiders, etc. But it could be there is no fault, and you clearly will not find a spider etc if no fault, the other method needs test equipment which you don't have.
Much depends on how happy you are going into a consumer unit, in my own house I would test, but if I was for example stuck in a remote house on the Falklands with no meters, I would one by one disconnect the circuits including the neutrals which means going inside the consumer unit and that OK on the Falklands where I can turn off the generator, but most UK houses don't have a isolator outside of the consumer unit so even with isolator off, you still have live parts.
So yes turn off isolator and check out building etc, but once the basic has been looked at, then you have two options, continue resetting and cross fingers and hope it goes away, or get in an electrician, and you need to consider do you really want so many circuits on a single RCD, or do you want it modifying?
My son has my old house now, and it still has two old Wylex 4 way fuse boards fed from two RCD's with the fuse carriers swapped for MCB's, as it has been for around 30 years, however it is on his to do list to change to a single consumer unit with all RCBO the same as this house, but one thing about having RCD protection for 30 years I know from experience some times they do trip and no amount of testing will show the fault, and it simply goes away, think in my case it when away when the welder next door sold his house and moved out, think it was spikes from him welding, but could never prove it.
