OK I’m not an electrician, but that sort of RCCB (the big switch) with a 100mA+ rating won’t save your life in event of an earth fault through you. You should check with an electrician, but I am pretty sure the RCCB does not provide overcurrent protection either, e.g. in even of a live/neutral short. The 80A I believe refers to how much current it can handle whilst still operating as an RCD. Over that current (even with a transient) and it can damage it permanently and prevent it working correctly
Check with an electrician, but for great protection you have a couple of choices. Ideally change out the RCCB for an 80, or 100A Breaker and replace every MCB with a correctly rated RCCBO. The box has a din rail and although not a cheap fix will give you ultimate protection, with minimum nuisance tripping. The Crabtree RCCBOs would cost you £30 each, an electrician will get them cheaper and might pass some discount to you. If you’re not fussed about having Crabtree ones, as it’s a standard DIN rail fitting, you can get other makes for around £15 each..
The suboptimal, but cheaper solution is an 80/100A breaker again depending on your incoming fuse and a separate RCD rated to 80A and 30mA. If there is space inside the box to fit (not sure their is)…don’t know if they make 80A overcurrent breakers and RCDs combined to act as fusebox circuit breakers.
The above is based on the assumption that you don’t have a separate 80A breaker feeding that fusebox!
I’d strongly recommend you find a good sparky and get some advice, simply because that installation needs some work.
As for the machine, if it’s tripped the MCB anbd then the RCD, it may be a badly blown heating element, direct short, or even a reasonable earth leakage, from what you describe happens.
The more important thing is to get the consumer unit looked at!!
If it helps, this is what I had installed as one of my consumer units