Even if planning permission is granted, the project cannot go ahead unless all affected leaseholders sign a License to Alter, which is drawn up by the Freeholder’s lawyer (paid for by the property doing the building work).
This, and a party Wall agreement described in detail by M below, provide clauses setting out, among other things, the times when work can be done and indemnifying all the other leaseholders against any damage - it will all be repaired and made good. They are maybe the best way you can safeguard your mum’s wellbeing.
It’s a pity she has this to deal with at the age of 96, in her family home of 60 years. It can’t be easy for her.

Your poor mum!
Your first step must be to see if you can oppose the planning permission being granted in the first place. Your mum should have received a letter about this too, or there should be a notice on a lamppost not far away, which will have the details of the case number and how to object? Hopefully the freeholder can help you there too, as they should have been notified.

If the planning permission is already granted (or goes on to be granted )and they are going to start the work, then a party wall surveyor could help. I should qualify my advice that I am not sure about the situation where it concerns an upstairs flat. The flat next door to mine is doing substantial building work and I did appoint a party wall surveyor. This is paid for by the person doing the work, ie the neighbour, as my party wall will be affected by the work. The surveyor advised me about the detail of the plans. He took photos of my property in advance, in case any cracks or damage appear later. He drew up a party wall agreement, which outlined the level of acceptable noise etc and the extent of any consent that I was prepared to give or withhold to scaffolding and access for their builders. They couldn't start work until this was completed. The surveyor has also intervened when the builders were drilling at a time when they shouldn't.

I hope this may help you a little and may reassure your mum? I don't know if a ceiling can count as a 'party wall' but perhaps have a preliminary chat to one of the surveyors and see what they say. They ought to take into account the age of your mum and her being housebound when they decide what would be reasonable or not. If you want a surveyor recommendation, I can recommend the one I'm using (although he's based in Fulham). Good luck!

Hi My 96yr old mother has lived in her ground floor maisonette for over 60yrs in SW17. She has been housebound for the last 6 years, limited mobility and a heart condition. The upstairs neighbour has applied for planning permission for a mansard roof extension to the main rear roof with French door & safety railings and a gutter extension above the 2 story back addition with a 1.7m screen surround. We found this out as my mother received several letters via post offering services from party wall surveyors. I’ve looked on the Wandsworth council website and cannot see the plans. We are obviously very concerned about mum staying in the property whilst the works are in progress, but she is unable to move out as it would have a detrimental affect on her health, the upper flat is also leasehold. We have contacted the freeholder to see if they can provide further details. My mother owns both the front and back gardens and has done since she purchased the property in the 60’s. Not sure what we can do to legally with regard to noise, disruption, scaffolding. It’s worrying her sick and making her quite unwell. Any advice would be much appreciated. Thank you