16A RCBO triping

Hello The RCD element of the RCBO is detecting a earth fault which the old rewirable fuse wouldnt detect, it's most likely the Element on the washer/dryer?, the Electrician who swapped the fuseboard should have given you full Certification with the Fuseboard change with Test results from the circuits, assuming these tests have satisfactory results it can only be what's plugged in or wired in to any fused spurs on the circuit in question. Putting a higher rating RCBO on wont change the tripping as the RCD element will still detect the issue. The issue is with the appliance I think you will find, if the machine is plugged in pop it on a extension lead and run it to another circuit and as long as that circuit is on a RCBO you should find it will then trip that circuit which would prove the issue is the appliance. Hope this helps.

Over load

Well it seems there are few more things need to be taken into consideration other than RCD element, new RCBOs normally they are 16 amps, in your case it seems you have 15 amps RCBO an other thing which I have also noticed your washing machine rating as you described it takes 1Kw but when it spins and dry it takes 6.5 Kw. Now we need to figure out, do we have earth leakage fault or over load problem? If you turn washing machine on, it trips straightaway then it could be earth leakage fault your RCBOS RCD element is there to detect earth leakage depending on type and maximum earth leakage it can take even though there are RCBOS available starting from 10mA but they are not commonly used, we still tend to use 30 mA RCBOS they capable to take up to 20 mA earth leakage current and they won't trip, but if earth leakage current is around 23 mA it could detect earth leakage fault and it can trip, it isn't big deal we can find  out amount of earth is leaking by using earth leakage test meter. Now if your RCBO is tripping when it is spinning or drying mode then this could be potentially overload issue as for 6.5 Kw we need 32Amp RCBO and cable shouldn't be less than 4mm2 with the exception of ring main circuit.

6.5kw? That’s around 28amps with new 230v working out. As other poster said try it on a different circuit and see what happens, but if it’s 6.5kw you will need a bigger breaker either way