Neighbour (leaseholder) won't fix damp

Kandyscat

My mum lives in a flat and bought her freehold last year. The neighbour downstairs due to them in serious debt couldn't afford their share, so we bought that also. 

Their flat has 58 years left on the lease.

Our problem is their flat has damp/mould. Despite them having a garden, they've been drying their clothes indoors (they even have a washing line in their hallway)

They no longer use their bedroom because of the problem. 

My issue is that we're now starting to smell the damp upstairs. 

I have a damp surveyor coming next week to assess things in our communal hallway and in my mum's flat. 

My mum, who is 73, has already had four strokes and a heart attack, so it is vulnerable.

I've spoken and written to my neighbour and asked them to get it rectified. But they've ignored all contact. 

What can I do? 

ThisIsWeird

As the Freeholder, you have a responsibility for the maintenance of the building's 'structure'. In addition, if the smell is causing a nuisance, then you have rights there too, and should tackle that via your LocAuthority.
But, is either of these situations the case? You can smell the damp coming from the other flat?
What's the situation with the occupants? Are they elderly or infirm? Is there a 'reason' why they don't air their clothes outside in nice weather? I presume the reason they don't use a TD will be cost.
Do you have contact with them? Are they approachable? 
It is quite possible to dry your clothes indoors using a horse, but it needs to be in a well-ventilated room. Ie, with the windows fully open, and a stiff breeze flowing through. Do that, and there should be no mould.
It sounds as tho they don't ventilated properly, or at all, presumably thinking that cold air will make the matter worse - it won't. 
If they also avoid their bedroom, it sounds as tho' the mould it bad enough to be a health hazard to them. 
See what the surveyor says - if they agree that the damp and mould is causing an issue to a communal area, or to any part of the building's structure (eg ceiling/floor joists), then that should theoretically give the Freeholder the right to act, and force the LH to take remedial action.
Regardless, there may be valid reasons here to contact social services - def so if the occupants are young, elderly, or vulnerable. Actually, in all cases - bad mould can be quite serious, I understand.

Does the buildings insurance, which presumably your mum arranges, include Legal Cover?