I wonder why an electrician has not tested to find out what is faulty, for a RCD to trip, the current in does not match current out, in the main this means some current is going to earth, however as
@ianmcd is asking some boilers have electronics which means there is a DC component to the current so a type A rather than normal type AC RCD is required, I know Worcester Bosch ask for a type A with some of their boilers.
Also in many houses there are many circuits powered with same RCD, in my case I have 14 RCBO's which is a RCD and MCB combined, so when one circuit fails it does not affect others, but where one RCD feeds many MCB's then it is a case of getting the insulation resistance meter out and actually test, as many items can all have a slight leakage, and the central heating may be just the straw that breaks the camels back. There is also a clamp on meter, but for the clamp on meter to work, it needs to be below the trip threshold.
The RCD should always be testing when changed, the strain on the cables can cause it either not to trip, or trip too easy, so the RCD is tested 6 times, three tests but each done on both positive and negative half cycle, so check it does not trip on half rating (15 mA) then check does work at rating (30 mA) then test at 5 times rating and must trip within time (40 mS) clearly can't measure 40 mS with a stop watch, so needs proper meter, this testing must be done when a RCD is changed. However I have seen where a RCD is tripping and it passes all tests, but swap it and new one passes all tests but does not trip.
However it is not cured by randomly swapping parts and crossing fingers.
Fact it does not trip with earth disconnected does point to the boiler, unless disconnecting boiler earth also means earth disconnected from some thing else. There are signs on the RCD
this one means type AC which is standard, but
this means type A which some boilers require. Even with RCD's of same type, not all equal, there are some which give a warning first then trip at 90% instead of 50% unfortunately they called them X-Pole so when you hunt on internet you get pole dancers.
I did get a rubbish electrician at mothers house, all he had was a multi-meter, clearly not a scheme member as they are forced to have all the test equipment, from what you have said it seems the electrician either does not have the test equipment or does not know what he is doing? Because it needs calibrating it is normally supplied by the company, not personal tools, and some companies are tight, and make electricians share the equipment.
Also in the main items are tested using 500 volt, however this can damage some items so we also have a 250 volt setting for sensitive items like a boiler, so the guy does need to know what he is doing, the 500 volt will not kill you as very low amps, but it would give you a nasty shock, so normally electricians work in pairs where doing inspection and testing.