I had a similar Asbestos problem to deal with a couple of years back when a builder I had asked for a quote refused to do the work as he believed that a ceiling in an attached double garage was asbestos. I also have previous experience in an industrial setting where removal cost many millions of pounds. I am however, no expert on the subject and my comments purely reflect my own understanding and experience.
One needs to keep a balanced view of the risks from Asbestos as they range from almost zero to considerable depending on type and handling. Many builders still ignore the risks as "I used it all the time and I'm OK, bit like smoking really if you are unlucky you are really UNLUCKY. Anyone who has seen the result of exposure to Asbestos will not take a risk with it or risk anyone they care about.
It is also very difficult to identify without a proper analysis as while the Cement types of products (Chrysotyle) are generally thought to provide less risk this is not always the case as they can also include the more dangerous (Amosite); the most dangerous (Crocidolite) unfortunately can also be present in some cement based products and was widely used in some spray on coatings as well as insulation for pipes boilers etc. You can remove Chrysotyle without any special approval and most councils will accept "domestic" amounts as long as it is double bagged and clearly marked. Personally I wouldn't even touch this type if it was damaged, flaking or broken up during removal. Anything containing the two other types will need to be removed and disposed of by appropriately licensed contractors.
I had mine properly analized at a cost of £120 and despite being told many times it was harmless it contained Amosite so needed appropriate handling. I was told that as it was in good condition it could stay in place and be treated as long as it was clearly marked, my wifes' response to that suggestion was unprintable. This is where more trouble is waiting as many companies use the "Asbestos" factor to ramp up prices. The quotes I obtained ranged from £2.5K to well over £6K for the job. On personal recommendation I chose a local company at £2.8K and they provided a superb service including dealing with all the paperwork and local council etc.
So, down to you really if it is actually Chrysotyle and is removed correctly then it might be a very low risk removal and should not incur too much expense but I wouldn't touch it without a proper analysis.
Keith