West Suffolk MP and former Health Secretary Matt Hancock has called for more devolution to "unleash the potential of Suffolk" - and for health and social care to be run locally.
The government is currently looking at plans to extend devolution deals in England - giving new powers to county-level authorities, although whether current county council structures would be retained is not clear.
Mr Hancock told this week's Westminster Hall debate on levelling up in East Anglia: "Through devolution, we can help to level up.
"In Suffolk, there is support from the county council, the district council and all the MPs. That devolution should include the devolution of health because there is no greater levelling up than in health."
He said that combining health and social care in the deal would improve people's lives and their economic prospects: "That is what levelling up is all about."
Government minister Neil O'Brien from the Department for Levelling Up said the strength of local government had been shown during the pandemic - and while nowhere had got everything right, it had fulfilled a very important role.
He said there had been a failed attempt to get devolution across Suffolk and Norfolk a few years ago (which was accepted in Suffolk but rejected by council leaders in Norfolk) but now there had been some strong county-based bids.
He added: "Nothing, including health issues (raised by Matt Hancock) is off the table. That could be a big win for the devolution agenda."
Exact powers for devolution would have to be agreed with the government and the structure would also have to be defined - in many places it has been accompanied by a directly-elected mayor.
Another issue that would need to be decided is whether policing would be included in a devolution deal - in some places police administration has been included but in others the role of police and crime commissioner has remained separate.
The prospect of devolution returned last summer when the government announced it was planning to publish a White Paper on the subject in the autumn.
That still has not arrived - in November ministers said it was expected to be published in January but so far there has been no sign of it.
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