The King's Fund says that work still needs to be done despite the recent government survey painting a picture of patient satisfaction.
The Department of Heath survey found that 84 in every 100 patients were satisfied with their GP practice's current opening hours.
But King's Fund Chief Executive Niall Dickson said that while these results are encouraging, "the picture of high quality care is not universal and some patients and communities in England continue to get a raw deal."
There is still room for improvement, he says, and the survey does not mean that primary care is immune from reform.
"Today's findings show that there are major challenges in deprived inner city areas with minority ethnic groups in particular suffering from poorer services," he adds.
"People who live in urban rather than rural areas and those from non-white ethnic communities are less likely to report that they are satisfied with their access to GP services."
Mr Dickson says we should not get complacent, as one in four patients report that they could not book a GP appointment more than two days ahead and one in five could not easily get in contact with their surgery over the telephone.
A significant majority, he adds, also want GP opening hours to be more flexible, including opening up during the evenings and weekends.