We have just bought a house which has/ had some asbestos in it. We had it in old vinyl under the carpets and we also have an asbestos cement downpipe or two on an outbuilding.
I am writing this not as an asbestos expert but as someone who did a fair amount of research when considering how to deal with ours.
First off, asbestos is so common, I would think that the majority of buildings built after the early 40s and before it was banned will contain it somewhere. Many householders (and that includes me and all my family!) are not aware of it. Common locations are in the loft, ceiling boards, soffits, garages, cement rainwater pipes etc, old floor coverings, backing behind fireplaces, in artex wall and ceiling coverings... It's usually fine if left undisturbed and if it's undamaged, and can be sealed safely if you know what you're doing and don't plan to disturb it in the future. Disturbing it includes drilling, sanding, cutting, scraping and of course demolishing etc.
Removing asbestos yourself is really not a good idea unless you are following HSE guidance. Licensed contractors (licensed by HSE, they have a list of ones local to you) will do the job safely (you would hope) and it mightn't be as expensive as you think. For testing and the safe removal of asbestos-containing flooring throughout our 3-bed semi and taking away two seriously heavy, ancient storage heaters which also contained asbestos, we paid around £700.I think perhaps that was going a bit but we needed it done at 24 hours notice because the carpets were due to be fitted the next day
. OUr type of asbestos wasn't particularly dangerous but I wouldn't have done it myself -you would have to buy special masks (not just dust masks), suits, and tape off your working area, as well as hoover up with a special HEPA-filter hoover afterwards if you're going to do it properly.
Asbestos cement I think is considered lower risk. OP you say the ceiling boards are made of this but they could also be asbestos insulation board which looks similar but is really not nice stuff and needs careful handling. The only way to be sure is to test it properly with a lab that specialises in that sort of thing.
Just to clarify, there are several (not just two) types of asbestos. Blue asbestos (crocidolite) is considered the most, not least, dangerous. Brown is also considered significantly risky, white a bit less risky I think. Danger level depends not only on what type of asbestos it is but also on what condition it's in and how 'friable' it is - e.g., how well-bonded it is and how many fibres are likely to be released when it's disturbed.
I would ask a licensed contractor around to the property in question and get them to give you advice on the best thing to do with your asbestos - it could be it just needs sealing which will be minimal cost.