What different needs?
Wherever someone is in the UK, they all have the need for easy access to timely and good healthcare (and other essential public services).
If you mean, there's a higher proportion of wealthier people in Weybridge than in Bolton, a) Wealth doesn't prevent ill health. It helps yes but wealthy people still get sick or have circumstances (eg. DV) that require healthcare or other support.
Also in generally wealthy areas, poverty still exists. Just often more ignored because people generalise about areas. So sometimes less help available precisely because of those stereotypes.
A good example actually of how one size fits all being applied to local areas failing people.
And there's the social cleansing issue. Vulnerable older people are more likely to be isolated (a health risk factor) because their children - family support network - have been socially cleansed away from them.
Re local councils. I don't think they should be scrapped (they represent the local areas) but I do tink all essential public services should be provided on a national level - with equally good access and quality - across the UK.
Personally I'd scrap council tax, and increase income tax instead. Possibly though keep some form of local income tax - to be used for local nice-to-have but not essential services or facilities.