You seem to have some knowledge of electricity. As a fellow DIYer, I think it would be reasonable for you to so some careful investigation on your own. Obviously, choose the right moment, for the family, to switch off the main isolator and have a look inside the CU. Be aware that the large grey phase wire going into the main switch assembly can carry a lethal current and if you can see any exposed red sheath under the grey cover or even, God forbid, any exposed conductor, STOP, and put the CU cover back on. Call out a lecky, because the CU is unsafe and the Main Isolator Fuse (as I call it) on the supply cable going into the CU needs to be removed by an authorised person to properly refit that phase wire.
Assuming the CU is safe, you can check the size of the wire to the lighting circuit as a a basic start. You might know that MCBs are categorised into 3 types: B,C and D, whereby the letter indicates how quickly the MCB reacts to overloads. B is the quickest, C is medium and D is slow (too slow for domestic use) Wiring regs require lighting circuits to be isolated within 5 secs of a phase to earth fault. See the Wiki for more details. I guess the 5 secs is there to allow for continuous switching of lights (current surges) and the fact that no-one is expected to be handling lamp holders on the ceiling, etc, so injuries are not expected if the circuit is properly operated (ie not handled).
MCBs are easily removed. They are usually clipped onto a DIN rail. It should be obvious how to do it once they are exposed. Even though the main isolator will be off (because you did that to begin with) I strongly suggest you check throughout the CU for any stray voltages with a multimeter before you put your hands in there.
It would be sensible to change the MCB like for like as far as manufacturer is concerned, but you could simply take the old MCB out and take it to the wholesaler and get one of the same design. The rating of the replacement needs some thought. Here's my thinking: despite the 5 secs time limit, you should aim for a quicker disconnect (B type) if any lamps on that circuit are wall mounted and easily touched or in areas of heavy people traffic. ie if there is any chance that someone might knock it of the wall and create a short to earth it must disconnect ASAP and a B type is the better one for the same current rating. If all the lamps are out of normal reach, a C type is good enough. Given that a C is more resilient to overload, you could fit an MCB that exactly matches the max potential load. If you need a quick disconnect you will need to get a B type that will be resilient to surges at max potential load, so a B 10A will probably work with your 1.8kW max load.
I don't think this is notifiable, but it is a minefield.
Doubtless a qualified spark will comment on my DIY approach.......