RCBO are essentially a combined RCD and MCB, so it could be an earth leakage fault, or it could just be faulty. It could also be that the new pump has a higher start-up current demand.
Unless you have an RCD tester (and probably a Megger/Insulation tester), you’re probably going to need an electrician to narrow down the problem.
As for fuses. The 13A rating is the continuous rating. For the fuse to blow, it requires being overloaded for a period of time. The higher the overload, the quicker it will blow, but unless it’s a big overload, it can take many seconds for a fuse to blow (I’m sure a bit googling will turn up the BS spec for domestic fuses).
A MCB/RCBO is likely to trip faster, depending on what Type it is. Type A will pretty much trip instantly on overload, whereas Type B and C have increased overload thresholds, to allow for things like motors that have a high start-up surge.