It found that younger people viewed privatisation as a possibility but not necessarily as a negative.
Older people were concerned by NHS privatisation and feared ‘losing' the NHS.
The research also found that while people say they want a nationally based NHS, when asked how resources should be allocated in their area the public supports locally tailored services.
David Furness, health project leader at the Social Market Foundation, said: ‘Our research shows that people will accept local variation in the NHS if they feel their views are taken into account - fears about postcode lotteries are largely misplaced.'
- Are you worried about NHS privatisation?
More news from 16 July