What cancer patients get depends on whether they have treatment in hospital or at home (via tablets). As she is having hospital-based chemo, Carol should be getting a decent amount. (A friend of mine, who had the tablet-based chemo - which didn't work - was assessed fit for work three weeks before he died.) But it's still not going to be enough, though, especially in London.
Bianca should be claiming Tax Credits in order to make up the shortfall for her kids. Never heard this mentioned, however.
My brother has learning difficulties and has recently had to start paying council tax out of his (very basic) Income Support. If he didn't have my mum paying for stuff for him, life would be very grim.