Some, actually most, of these replies are just nuts.
For goodness sake, OP is doing a bit of cleaning for her own mum and a couple hours for her mums elderly neighbour and getting a few quid in hand for it. Less than £1000 a year. Because times are tough and they need food and electric. Not so she can spend weekends on her luxury yacht in the med. She's hardly starting a billion pound company and avoiding paying hundreds in tax! Have none of you never ever done a simple job for a friend or neighbour and been chucked a could of quid for it? Or hired a mate to do something and paid a little less 'for cash'?.
Gain a little perspective.
Honestly, yes of course it should be 'declared', but shes hardly going to bankrupt the country doing a couple hours cleaning for 2 elderly people, one of whom is her mother and the other her mothers friend. It may well not affect her benefits anyway. Well, it shouldn't. Surely its better for OP to be out doing something and keeping her off the bread line than sitting at home doing nothing. If she turns it into an actual 'business' thats different. But for less than £100 a month, shes hardly retiring anytime soon.
If I knew someone who had a host of medical issues and was doing a couple of hours a week cleaning for a friend or relative in order to be able to put food on the table, no way would I report them. Its such a small amount, but makes a big difference to OP. If that someone was cleaning everyday and running a business while claiming benefits, thats a totally totally different scenario!
As for poaching clients. Again, its OPs mother! Would you seriously not give some cleaning work to your own child over a stranger if your child needed the money to survive? Same for the family friend next door. OP didn't poach clients, your friend is being ridiculous OP, although I can see she may be a bit annoyed at losing the work. If you were actually starting a business up, I can see her point, but you are not so shes being ridiculous.
I hope the cleaning works out for you. And I'm sure its doing you a world of good just getting out of the house, and helping to pay the family bills.