A senior Tory MP has called on ministers to "stop the cuts" to public health budgets.
Dr Sarah Wollaston, the chairwoman of the Health Select Committee, said reductions in funding will "severely impact on the Government's ability to tackle health inequalities".
Meanwhile, Labour's former health secretary Alan Johnson urged Theresa May to take personal responsibility for reducing levels of health inequality.
Leading a backbench business debate on the issue, Dr Wollaston said: "Preventing early deaths we need to look at all those lifestyle issues around smoking, obesity. We also need to look at issues like preventing suicide, the greatest single cause of death in men under the age of 49.
"We also need to look at how public heath plays such a critical role.
"We know that the five year forward view called for a radical upgrade in prevention in public health and I think one of the disappointing things that we have seen is cuts to public health budgets and I think that that will severely impact on the Government's ability to tackle health inequalities."
Dr Wollaston highlighted issues within her own Totnes constituency in Devon as she said cuts were resulting in healthy lifestyle services being scrapped.
She said: "I really regret that those will be going ahead and call on the Government to stop the cuts to public health."
Meanwhile, Mr Johnson said the Prime Minister should put herself in charge of reducing health inequality.
"I believe the Prime Minister herself should take personal responsibility for this issue," he said.
"The Prime Minister is also First Lord of the Treasury and also the minister responsible for the civil service.
"Previous prime ministers have taken on other ministerial positions. Wellington was foreign secretary, home secretary and defence secretary and commonwealth secretary.
"Churchill was prime minister and defence secretary.
"It would be a wonderful example for the Prime Minister to follow up her words by saying 'I'm going to lead on this, I'm going to chair the cross-government committee that tackles health inequalities'.
"I think it needs that level of leadership."
The Government unveiled its childhood obesity strategy earlier this year and Dr Wollaston said she welcomed the measures within it but suggested it could have gone further and currently has "glaring deficiencies".
She said she wanted to see a "far greater emphasis" placed on tackling the marketing and promotion of unhealthy products and for the sugary drinks tax to be extended to other drinks.
She also urged the Government to follow Scotland's lead and seek to introduce minimum pricing for alcohol.
"I think it would be a great shame if England were undermining potentially groundbreaking work in Scotland by allowing people to buy across the border," she said.
"I think it will be a great shame if we don't follow suit at the earliest possible opportunity and introduce minimum pricing."
Labour MP Alex Cunningham (Stockton North) said he feared that health inequalities will rise as Britain feels the squeeze following Brexit.
He said: "We had one of the gloomiest outlooks for our country from the Chancellor for decades when he spoke yesterday in the Autumn Statement.
"He spoke of the uncertainty ahead, of rising debt and borrowing and falling growth and tax revenues.
"My great fear is that in the tough years ahead, coupled with the failure of the Government to properly fund public health, the NHS and social care, we will actually see health inequalities grow not reduce."
Meg Hillier, the Labour chairwoman of the Public Accounts Select Committee, bemoaned the way public health budgets are being treated.
She said: "There is not an openness about discussing how we spend money on the NHS, what we spend it on and what we focus on.
"That brings me to the issue of public health.
"We are seeing public health budgets raided to deal with day-to-day crises too often."
Copyright (c) Press Association Ltd. 2016, All Rights Reserved. Picture (c) Peter Byrne / PA Wire.