Labour and Liberal Democrat members also agreed not to campaign to give Dr Irvine the best chance of taking the seat from Mr Hunt.
The Labour Party faces "a huge challenge" over the remainder of the general election campaign, Jeremy Corbyn said.
Mr Corbyn said that in the coming days Labour would be spelling out the details of a "plan for Britain" to transform the country and change an economy which was "still rigged in favour of the rich and powerful".
His comments were criticised by the Tories and Liberal Democrats and according to the Telegraph caused angst among some Labour figures.
Some hospital trusts have allowed parking charges to soar to shocking levels in recent years.
Last month, a Freedom of Information request by Unison revealed some hospitals are charging staff, including nurses, almost £100 a month to park, resulting in nurses having to rush out between appointments to move their cars and avoid fines. "We're not proposing to raise Value-Added Tax or national insurance".
It would mainly hit corporate employers, who buy 80% of private medical insurance policies, often on behalf of wealthier high-skilled workers, Labour said, citing research from healthcare consultants LaingBuisson. "Scrapping paid-for parking is the right thing to do for staff and patients alike".
McDonnell, a key ally of Jeremy Corbyn, said the party must bounce back from the loss of hundreds of seats in council elections.
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"There would be less money to spend in hospitals, not more".
"Labour wants a jobs-first Brexit, a Brexit that safeguards the future of Britain's vital industries, a Brexit that paves the way to a genuinely fairer society and an upgraded economy", he said at the campaign launch in the northern city of Manchester.
East Kent Hospitals University NHS Foundation Trust and University Hospital Southampton both made more than £3.3m in the same year.
"But expecting distraught families and underpaid staff to make up the difference through extortionate parking charges is not the answer".
"Now is the time to put everything else aside, to stand up for what you believe in in your heart and soul, to get out on the streets, get this message across loud and clear". Only by progressives working together can we beat the Tories.
Parking charges at hospitals, levied by cash-strapped NHS trusts, have reached record levels in England.
Having faced criticism for being unclear of his position on Britain's divorce from the European Union, Corbyn said the issue of whether Brexit should happen had been settled, and went on to set out his negotiating objectives.
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