When you say you have applied, what stage has the application got to?
I used to work for our social services' occupational therapy team (the people who co-ordinate all this stuff). They will have to make an assessment visit before passing on their recommendations, which have to be approved. Cases have to be prioritised because there are just so many of them (we'd get something like 20 or 30 new cases a week). From what you say, your case would be classified as top priority, but even then there is a considerable wait, depending on which council is involved.
Basically, we don't have enough social workers and OTs to cope, and that's because councils will not allocate funding to employ them. One of my previous bosses, one down from director level, told me that there is plenty of money there, but SW's etc. are all told that there isn't. I was applying for some mobility aids for my mother at the time, and the guy basically told me to keep on at her council if nothing happened. Nag them to the back teeth if I had to.
What we did find was that clients who complained to their councillors got dealt with more quickly. Departments jump to it pdq when a councillor complains. Not fair, I know, but it might be worth a try.
My mother is currently waiting for a bathroom adaptation, which should be happening in the next few weeks. It's been around six months since we first contacted SS. The OT had to come and make a full assessment. Once that was approved, she had to have an architect and some sort of buildings adaptations officer to come and draw up plans. Then it had to go to tender. Last week saw the plumber's visit and, like I said, he should be starting work within the next few weeks.