It's news to me that people are clamouring to live in Barnet
They're clamouring to live anywhere in the SE. There's just no social housing, I'm aware of people who are long term London residents with disabilities who have all their support network there being told their only option is Birmingham or Newcastle or a 15 year wait in temporary housing minimum. People are ending up in expensive, too small, insecure unsuitable for their disabilities private lets or sent hundreds of miles from everything they've ever known and vital support networks.
It sounds to me like these two women are trying to jump the queue for housing in the SE by creating this situation to use as leverage for housing priority. Especially given the daughter is now attending college in Barnet so they clearly never had any intention of returning to Lincolnshire, making long term commitments in Barnet.
I'm really glad the hospital has called their bluff and refused to involve Barnet Council. It's easy to say 'Oh just give them somewhere', but in reality that would be shoving people in Barnet with just as bad illnesses and disabilities who are homeless and in temporary accommodation further back in the queue purely because they've applied honestly rather than engineering a situation they don't think the authorities can say no to.
I also think it's incredibly smart of the NHS to realise it's cheaper to put up this one person than let the scam work and deal with the fallout. If they'd succeeded with this word would have spread. Every person with a disabled relative who wanted to live in London would be turning up at London Hospitals with a poorly relative then announcing they had nowhere to go at discharge. It would cause massive disruption if it spread, and this sort of scam spreads quickly.