Our bathroom has 4 downlights in the ceiling. For some time only 3 have worked – checked the bulb and it wasn’t that. Now a 2nd light has gone and again it’s not the bulb. Looking into the ceiling recess it appears that something has got very hot as there are black scorch marks on the connector blocks of both lamps that have failed. Also the metal surrounds that screw on to the remaining two working downlights to hold the bulbs in place are very hot – is this normal?

The bulbs are either MR11 or MR16.

transformers burnt out?

replace the whole lot with GU10 240v LED downlighters

Not normal, probably the transformers sitting in the ceiling space have gone pop.

Get an electrician to look at it as you dont want problems with electrical equipment in a wet enviroment.

assuming you have MR16 12v halogen then yes, it will get hot.

LEDs run much much cooler and safer IMO.

Thanks do these things have one transformer or one per bulb?

depends on specification of bulb & transformer. Some used to be 1 to 1, others might run up to four. Since you have lost one lamp then a second one Id suggest you have 4x transformers. (although I am wondering if there were transformers that have more than one output channel? Probably not.)

Kill the juice and have a good rummage around – the transformer ought not to be too far from the bulb holder up the line. With any luck you might have enough mains supply cable once removed from the transformer to connect to a new GU10 lamp holder without any further mucking around. If not you will either need to be a confident bodger 😉 or get a proper sparky in.