In Canada she is what is called an "alternate level of care" patient. Which means she is taking up a hospital bed although she does not currently require the acute level of care hospitals are designed to provide.
I'm unfamiliar with the numbers in the UK. So I don't know how dire of a situation ALC patients are considered to be there. In Ontario, where we have both a shortage of long term care beds and a shortage of hospital beds, ALC patients are considered to be a very bad thing, and hospitals will try to do whatever they can to discharge them. In my personal experience, this includes attempting to bully family of the patient into taking them back home, even when they know caring for the patient in a family home setting is 100% unviable.
For example: when my mother was designated ALC, the hospital tried to bully her son into taking her into his home until an LTC bed became available for her, even though his home situation was: two adults both working full-time jobs, two teenagers both attending school full-time, a half-flight of stairs just to get into the house, and no space for sleeping on the main level of the house even after navigating those stairs, and our mother's situation was: incapable of walking, incapable of feeding herself (she was being partially tube fed and partially spoon-fed puréed foods at the time), considered at high risk of aspirating whatever foodstuffs she did take by mouth, incapable of bathing or dressing or toileting herself, and unaware of what country she lived in, what year it was, or the fact that her husband had died 6 months previously. Nevertheless, individuals at the hospital told her son he had to take our mother home until an LTC bed became available.
He refused.
The hospital then came up with a list of three different transitional care facilities (designed for providing temporary care to people like our mother, who were on waiting lists for an LTC bed). None of them were suitable for a patient in our mother's condition. (One had patients in private rooms and required them to use a pre-programmed speed dial # on a cell phone to call for assistance. Our mother did not even know how to use a cell phone before an aneurysm ruptured in her head and fried her brain! Another flat out stated in their literature they did not accept patients with feeding tubes. The third I think only accepted patients for a maximum stay of 10 days, but we were being told it could be months before an LTC bed became available.) Still, the hospital told her son he had to choose one of the three options.
Again, he refused.
It was an extremely stressful time, and he had to take a bunch of meetings and phone calls with entirely unhelpful and threatening people. He delayed said meetings as long as possible to buy some time. And an LTC bed miraculously came available for our mother within only a couple of weeks.
Because ALC patients are considered the highest priority for placement in a long term care home.
So my advice to you is: do NOT under ANY circumstances, agree to take your former housemate back home. Hold strong on this, no matter how nasty the hospital staff get with you. They cannot kick her out onto the street. They are obligated to continue providing care to her until they secure a more suitable care situation. You need to remain firm that you doing everything by yourself 24-7 for a person who requires more assistance than one sole caregiver can possibly provide is NOT a more suitable situation. It's not even a viable situation. And the fastest route to a long term care home (which is the level of care she actually needs) is to remain in a hospital bed until an LTC bed becomes available.
If you think you have any powers of persuasion with your former housemate at all, you may want to try to convince her to be more agreeable the next time a placement specialist pays her a visit, however. (I don't know the laws in the UK. But here there are financial consequences for patients who refuse to move into available LTC beds.)