Bathroom downlighters MR16 halogen to LED?

I wonder if I can once again get some advice from you good people.

We have a bathroom with 50w 12v MR16 halogen downlights, including one directly over the bath and one above the shower. Each downlight is connected to its own transformer, rated 35w-120w.

A couple of bulbs went, and while it's possible to still find MR16 halogen bulbs, it seems a better idea at this point to change to LEDs. Especially, as replacing one of the bulbs didn't get that downlight working again. The lampholder still seems tight, can't see any sign of damp, loose connections or damaged wiring... so I guess it's possible the transformer has gone?

Someone suggested retaining the existing fittings, but removing the transformer and replacing the actual lampholder with a GU10 one, then just using a regular mains voltage GU10 LED bulb. But is this safe in a bathroom environment??

The alternative I guess would be using MR16 LEDs and replacing the existing transformers with LED drivers/transformers. Which I guess is just as easy but more expensive - and there seems to be a lot of confusion over MR16 lamps being DC or AC and using drivers or transformers; seems like a whole world of hurt trying to decide what to use!!

Do the existing fittings have a glass cover over the 'bulbs'?

Yes, they have a glass cover which is part of an assembly that clips onto the bulb and then "push fits" snugly into the recessed housing. Hope that makes sense!

Then they are PROBABLY bathroom quality and POSSIBLY can be converted to GU10.

Make and model number please.

It's unlikely these fittings are earthed, as they are 12v, so you MAY need to earth these fittings now.

Photographs would help here.

They're Robus ones, don't seem to be earthed.

Thinking about it, apart from cost, and the risk of damaging the ceiling finish, would it make more sense to replace the downlighter fittings themselves with GU10 ones that are bathroom-suitable? ie take out the transformers and downlighter fittings and replace with new GU10 fittings.

Ideally yes, the lights were made to only have 12 volt inside, therefore they may not be as safe with 240 volt in them especially as the cable will pass through a hole in the metal

Ah right, sounds like the right answer. Presumably I can just remove the existing downlight and transformer and connect new mains voltage IP65 led downlight, hopefully I can get it done through the hole, since the space above the ceiling is extremely tight and hard to get to!