"Asbestos in the ceiling' is rather vague. Are they referring to the ceiling itself? Popcorn texturing? Insulation above the ceiling?
As for the danger level of asbestos, it all depends on if it is airborne or not. In its solid state, it's harmless. It's only when it's friable and turns to dust and you inhale it does it become dangerous. Even then, note that for it to cause cancer and the like, it takes a LOT of exposure and a LOT of time. Most people injured by asbestos were those that worked in asbestos plants and mines. So, while it is dangerous, there is no need to immediately panic when found in your house.
I'm going to assume the asbestos is part of the popcorn texturing. This wasn't uncommon and (AFAIK) the most common place to find asbestos in a lot of homes.
As long as no one touches it, it's fine. If it's painted, even better. Did the plumber expose a bit of the asbestos? Probably. Enough to be of any real danger? I highly doubt it. Enough to cause the insurer or city or code to force you to remove it? I have no clue. That's more of a policy/regulation issue.
If this is a rental, then removing will likely have to follow particular standards, and that usually involves a remediation crew that comes in, fully seals everything off, wets everything down, bags all the materials, vacuums with HEPA filters, and then carts it all off for you. Fairly safe, though potentially expensive.
The risk is someone could inhale asbestos fibers and develop health problems far into the future. It's impossible to estimate the level of this risk, yet you need to do so in order to decide whether to vacate or not. Furthermore, if fibers could enter your flat, even if you vacated during the work, the fibers could still remain upon your return.
If the contractor doing the removal work is fully qualified to do this sort of work, the risk to your family should be negligible, yet there is always some risk even if infinitely small. Only you can decide if you're really comfortable with this or not, and what an appropriate response is. This is of course difficult without hard data, but there just isn't any.
One thing you could do is some airborne monitoring. This is often done as part of removal procedures anyway. I've no idea of the costs, and it only reflects levels during the testing period, but it may buy you some peace of mind.
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It's not really that serious in most cases. In tile or siding, it isn't a hazard unless it is broken down, generating dust that you are breathing. Even then, a lot of tile is like 1% asbestos. If you can get it up without breaking it too much, you're basically fine.
Pipe insulation that is soft is more of a problem. You can probably do it yourself if it's a small amount. It may very well be illegal though. Get a respirator like this http://www.amazon.com/MSA-Safety-Works-817664-Respirator/dp/B0009XW3ZS, take a heavy plastic bag, tape it around the insulation so it's mostly sealed, and then spray it down with water so it's saturated and won't generate dust. Then remove it, dousing with water as needed. Seal it up in the bag and dispose of it lawfully.
I was an asbestos abatement hygienist for 3 summers, and I took airborne fiber readings of thousands of hours of removal being done. Although negative air containment systems were in place on those jobs, I had probably 10 concerning readings out of thousands.
Asbestos is like smoking cigarettes in my opinion. One day isn't going to hurt you. Every day for 5 years will hurt you.