My mother worked on this issue for years before she died.
First, all local councils need to audit their adult social care costs, and deep dive into all the existing contracts (if they can find them). It is very likely that money is "leaking" all over.
Second, local councils need to identify exactly what they need, and be firm about it. There are cases of crazy management of facilities and services all over the country, more so after COVID. This needs sorting out sharpish, and councils are going to need to resort to legal action if need be.
Third, local councils need to either build or encourage the building of low to medium assistance developments for the elderly: complexes with self-contained small flats, but with communal areas and maybe a cafe or bistro on site, with a 24 hour warden and/or nurse. This will take the pressure off the "home help" budget, where councils are paying carers to attend elderly people in their own homes all over a borough, sometimes up to four times a day, when really all those people need is someone to look in on them and check they are alright.
Local authorities that have taken the third route do not have an adult social care crisis.
The problem is that a lot of LAs are stuck in this binary of "expensive care home vs. keeping people in their own homes", when what we really need most of all is a middle way. Not everyone needs a care home if they can't quite manage in their own home anymore. Sometimes, they just need to be in a flat in a complex in an area they know, where there are no steps, some nice green space, and there's some community and stimulation around them that is easy to access, and maybe somewhere very nearby that they can get a hot meal.
And providing care to people in their own homes is very expensive. It means a carer has to travel to the home, spend an hour or so there, and then travel to another home, spend an hour or so there etc. It's wildly inefficient. If these people were all in the same community complex, carers who need to attend get three times as much actual care work done, purely because they are not driving around all day -- and any emergencies are noticed by the warden.
We have a number of these complexes in my borough. The waiting lists are over five years long, which is a long time for someone who realises at 82 they can't quite manage in their own home anymore. There's a massive demand for them, and dementia development rates are lower within them as are typical elderly injuries (such as hip fractures etc).
That is where I would start.