As for care facilities, if the need isn't that common (e.g. once a week), is that really more effective than an occasional ambulance trip? Plus the patient might very well prefer to spend his last year as close to his family as possible.
If this is happening once a week then it really seems there ought to be a better way to handle it.
Edit: if you also assume that an ambulance dispatch is usually followed by an ER trip, the cost balloons even more. Seems really hard to think that a 911 dispatch followed by an ER trip once a week is the best way to handle a chronically ill person at home.
The BIG difference with what you've described though is the layout of the UK is much denser than USA. The resources available and the nature and frequency of call outs will obviously be quite different.
Home visits are great for physical therapy or protocol based care. But again, they call 911 when anything significant happens.