Removing the boiler and then the rads should have no effect on the immersion system if a bit of thought is used.
It could have been either one of them. I'm guessing the problem is in the airing cupboard. I'd need a lot more information on your system to be sure though.
It's certainly possible to remove the central heating system and the boiler, but a couple of simple bypass connections may well be needed to keep the HW flowing.
Sorry, Tandh, but I can't say without sticking my head in your airing cupboard.
If I were a betting man, I'd guess that the first guy isolated everything so as to remove the boiler...... then neglected to ensure the HW was running. Taking off rads and the sink should not mess up the HW.