OP l am a Landlord.
It sounds like you have an appalling landlord, l suspect you will have ongoing battle with him to properly fix issues by past history.
Do not disturb the asbestos ceiling.
You must not stop paying your rent as you are legally bound by your tenancy agreement, he also is bound to keep the property in a good state of repair, if you stop paying rent you will have broken your agreement and will probably be evicted. Also you will struggle to get a reference needed for another rental property.
If you stay within your contract you will have all your rights intact, he will be in the wrong for not adhering to his side of the contract in a court of law.
My advice is continue paying the rent, give notice immediately in writing, then contact Shelter.org.uk to find out your rights in this situation....they will be able to advise you. Also google... tenants and asbestos... to find legal help if needed after speaking to shelter.
Below is information regarding a Landlords legal responsibilties regarding asbestos;
RESIDENTIAL LANDLORDS ASSOCIATION GUIDE TO ASBESTOS
Key Points
'' For all residential premises, whether houses or flats, a landlord may, depending on the circumstances, be liable to be prosecuted if anyone such as a tenant, resident, workman or visitor, is put at risk of being exposed to asbestos or is actually exposed to it. The landlord is under a duty to ensure that a risk assessment to assess the presence of asbestos and how to deal with it is carried out before any work, e.g. repairs, is undertaken. They can be prosecuted for failing to do so.
In addition to making sure that a risk assessment is carried out before any work starts, a landlord must use a competent contractor to carry out repairs or other work. Landlords cannot simply leave matters to contractors. A landlord still has his/her own responsibilities relating to asbestos. At the very least, landlords must check that a contractor is competent. Likewise, any information about the presence of asbestos known to the landlord must be passed onto the contractor. These basic requirements apply to small landlords but, because the dangers from asbestos are well known, this may not be enough, especially for larger landlords.
A landlord who is an employer or who is self-employed must ensure that the Control of Asbestos Regulations are complied with in the case of domestic premises, including common parts. Any contractor must also comply with them. These regulations require that a risk assessment is carried out before any work is started to see if asbestos is present and to ensure that appropriate precautions are taken to deal with any asbestos which is present.
Again with all residential premises, any landlord who commissions repair or construction work has to comply with CDM Regulations which include an obligation to notify the present of asbestos to any contractor where the landlord is aware of this.
Additional special rules apply to the common parts of non-domestic premises. This includes the common areas of blocks of flats and bedsits but these additional requirements do not apply to individual self contained units (e.g. flats) or to single dwellings. Whether or not work is to be done, the landlord is obliged to carry out investigation as to whether or not asbestos is present in the common parts and if it is there to monitor its condition as well as putting control measures in place. Anyone who may be at risk as a result (e.g. a contractor carrying out work) must be notified of the presence of asbestos. The measures must be kept under review, at least annually.''
Good Luck op hope that is helpful.