I don't think it is necessarily a child's duty to care for parents when they are old and infirm. If I had had a terrible childhood with parents who made my life a misery, I don't see why I should be expected to care for them in old age.
However, having had a fairly happy childhood and an OK relationship with my parents, I do thinkit's my duty to take at least some responsibility for their happiness and wellbeing. My mum and dad visited quite often and sometimes went on holiday with us. When dad died, mum came on holiday abroad with us for 7 years running. Now I visit my mum once a week even though it's a 3 hr journey each way and tiring. I do jobs around the house and do her laundry for her, and take her to hospital appointments.
However, I find my mum very difficult - always finding fault, never satisfied with things that I've organised for her, always niggling about something or other if we go out or go on holiday. When she stays over Christmas my nerves are in tatters by the time she leaves. Although I feel I should have her to live with us if her health and mental state deteriorated, I really don't think I could. I think it would either have to be the care home option or, as she has a reasonable amount of capital, pay for more support within the home.
If a parent is undemanding and fairly easygoing and there is a good parent/child relationship, I think a lot of adult children would be prepared to try out caring for him or her at home if at all possible. But I don't think it's reasonable to expect children to care for parents who have many physical needs - perhaps including incontinence - and difficult behaviour, maybe resulting from advancing dementia.
I think the Gordon Brown idea of making a one-off payment of, say, £10,000, which would cover your care home costs should it be necessary, is perhaps a good idea. If the payment can't be met during a person's lifetime it could be extracted from the estate after death. It would mean that some people would pay for care that they never needed or received, but my feeling is at least everybody would make a contribution and everybody would have the reassurance of knowing that, should they need residential care, they would receive it.
If I was as well off as Sheila Hancock I would have no qualms whatsoever in going into a care home. She can afford the best. As others have said, less expensive care homes are not necessarily very good.