@DevsAd Thanks a lot for your input, it made me think, and question, and call another person in to try and fix it. I trusted the first guy and went on the assumption that the whole flue would have to be relaid, and that being a second problem with flue, I thought it cannot be done right and thus electric is the safer option. Therefore, the other visits I had were for a quote for new installation only (they didn't even start they boiler).
After your questions and input I decided to call another person in to try and fix it, or at least explain to me why it cannot be fixed. The result is that this guy actually decided to check WHY the flue is leaking, and it turns out it is a problem with installation right near the boiler entrance. Basically, the previous company hung it a little bit too low, and rather than correct their mistake, they fudged the connections on the flue right next to it (see new picture). So the flue (probably) never had a proper, tight fit and it's a bit of a miracle (not) that it worked so long. Not a miracle because if it failed earlier I would have called in the people who f..d it up to fix it but hey-ho.
Apparently the rest of the flue looks fine - supported in the right places, right drop etc. Hopefully they didn't fudge it anywhere else (but we didn't see any moisture anywhere else around the joints).
Anyway, he said he can fix it - he will lift the boiler to correct place, and replace these few parts with new ones, and seal it correctly.
Despite all that mess and leak, apparently the boiler survived (again - brave little fella!).
I don't want to jinx it, but hopefully by the end of the week I'll have it up and running again. I'll report here once it's done, but in any case - thank you SO MUCH for your help here, it's been invaluable.
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