What's up there depends on the age of the home and how much the contractor cared when they spec'ed it. Most likely, the ceiling is some form of gypsum board that is then plastered, textured and painted. The result of water leakage on gypsum board is usually that the entire board starts to sag under its own weight; alternately, the outer layer of paper, along with any spackle, texture and paint, will peel away with the damp.
Unfortunately, drywall repair == drywall replacement. You have to cut away the damaged portion, fit and screw a new piece of drywall into that hole (using rust-resistant screws as this area already has a reputation for moisture), then tape, spackle, seal, texture, prime and paint.
On top of that, many types of ceiling texture such as "popcorn" ceilings are simply impossible to blend in with when you do a repair like this; tiny differences in the application of the texture along with the sudden stop/start to the old texture around the patch will make repairs obvious. To really do the job right, you have to re-texture the entire ceiling by scraping off the old stuff, smoothing the surface with sandpaper or plaster, then reapplying texture, priming and painting.
If you're going to do all this anyway, I would recommend replacing the entire piece of drywall that has been leaked on with a more water-tolerant product like backer board (DuRock, Hardee-Backer, etc). This product is normally used in areas where water and/or heat can be a problem, and are durable enough to get soaked without crumbling apart unlike gypsum board. These products are generally a different thickness than drywall so you'll need to level the ceiling with lath strips of the proper supplemental thickness on the joists. After that, installation should proceed much like with drywall (you may need to smooth the surface with more plaster; backer board is commonly used as underlayment for tile and so often has a mesh that grips thinset).
One thing I've been surprised at doing my house is that getting a plasterer is easier and cheaper than you might have thought. So, be brave.
Take down the bits of ceiling and wall that are in the way, drill proper holes in the joists and noggins for the cable runs and lay the cable in. Wire up the other end of the cable, then tape over the ends of the cable where the wall lights will go.
Next get some plasterboard -- B+Q usefully sell it in half-size sheets that fit in a car -- cut to the size of your holes (with little holes for your cables), and nail to the joists in the ceiling and the noggins in the wall. Don't worry too much if there's a few mm around the gap, it doesn't need to to be too precise.
Then have a plasterer put a "skim coat" over the top of the lot. He or she may even say it's cheaper and easier for them to do the whole ceiling or the whole wall. Stand back open-mouthed while they do the lot in a few minutes!
Oh, and I'd take @Tim Baker's suggestion of picking up the power from the switch. Given that you're in the UK, if the wiring was done in the last forty years this is going to be a pull switch on the ceiling, no?
(Usual disclaimers apply: be careful mucking about with power in the bathroom, it makes sense [and is required by the Building Regs] for a circuit that's going to a wet area to be protected by an RCD.)
Best Answer
Normally can lights are attached to the joists, so the housing itself wouldn't usually fall out. What is probably falling out is the trim piece that fits inside the housing.
If you remove the bulb, you can usually pull the trim piece out partially. Once you do that, you'll see a couple wires (look like coat hanger wires). If you squeeze those you can pull the trim piece out the rest of the way. Those wires are what hold the trim piece in the light housing. Over time they can lose their "springyness" and slide out a bit.
Just take the trim piece with you to a home store and you should be able to buy a replacement, or you might be able to bend the wires a bit to get them to fit in snugly again.