Yes it's asbestos cement 100% sure, do not worry, it mostly certainly isn't crocidolite and slim odds it contains amosite, you've got there chrysotile, the least toxic. A few mouthfuls will not kill you or give you untreatable cancer, but do not damage or disturb it any further.
I would make your landlord aware about this and I'd be a little angry he didn't take the time to find this out himself before leaving you to carry out routine maintenance (you're clearly a good tenant). If I was him I'd have paid to have it removed by a licensed asbestos remover and re-covered with ply + felt. The whole thing should not set him back more than £1800. Bit of a careless inconsiderate prick if you ask me.
I have notified my landlady haha. I actually live at a separate property, this one is currently unoccupied & I'm helping to get things done there. She was unaware it was white asbestos until I went onto the roof. It is cracked inside and has been resealed by myself and another guy who came round to do it last year. There are loose fibres as well. Fibres and dust amongst the moss I did grab off the roof (didn't brush as I had a feeling it was asbestos). Not to worry either, was using gloves and a face mask when i was up there.
I just wanted to make 100% sure it was asbestos & I've been confirmed correct. Cheers. As for asbestos, I know the white cement isn't too bad but crocidolite (blue) and amosite (brown) are worse. Saw a lot of the stuff growing up. As for lung cancer, it's not something i'm concerned about, it's Fibrosis of the lung, ie: asbestosis. I know plenty of folk that have died from it just because they worked in an office with it for a couple of years.
80,000 people die from pollution every year, (mainly diesel fumes). Just leave the roof alone.
Nitrogen Oxide is a problem, I know. I live under a flight path about 1km from an airport as well so I have kerosene combustion products from the Jet A1 and A2 fuel pumping out over head.