Can a single mum in London with a full time job find a place to rent?

Hello landlords,
my colleague / friend is in north London, currently living in her friend’s front room with her 5 year old son, while looking for a one (or two) bedroom flat. She has a full time, permanent job, has worked for the same company for 7 years, her salary is just over £30k, commission is c£10k on top of that, but she is constantly told that £30k is not enough to be considered (let alone having a son). What can she do? Any tips, please? Would you rent to her?
Thanks!

Surely this is one for social housing? May not make sense to work in her situation?

Well she would barely qualify for £1000 pcm !and I know there is not 1-2beds for anywhere near that