There are some nasty bugs about at the moment. I came down with a nasty virus just after Christmas which went in to a chest infection and I'm still not well now. Is it his own flat or rented? This is targeted at rental properties but some general info too:
https://england.shelter.org.uk/housing_advice/repairs/damp_and_mould_in_rented_homes
Damp will not do his asthma and chest symptoms any good. If he can't get a tumble-dryer, could he let you help do some washing for him or does he have a launderette nearby where he could get his washing done without having to dry it round his flat?
Does he have a decent sized freezer if relatives made up some batches of decent home cooked food which he can heat up to help him out while he isn't well? Maybe some bags of frozen veg and such to make it easy for him to have quick and easy, but more nutritious, food?
A decent sized de-humidifier sounds like a good idea, those little ones are good to show up an issue but don't do much to help.