He made the announcement while visiting student nurses in Worcester, a marginal seat that Tories have held since 2010.
This, it said, would replace the £162m that England's "underfunded" hospitals now raised from auto parking charges by scrapping the subsidy for people that can afford it, rather than charging people who cannot.
"Our hospitals are struggling from under-funding at the hands of Theresa May's Conservative government, but the gap should not be filled by charging sick patients, anxious relatives and already hard-pressed NHS staff for an essential service".
The party estimates the tax rise will be enough to cover the £162 million that English hospitals raise annually from auto parking charges.
"I hope that one day in the not too distant future the Labour Party will see sense and return to a more moderate form of social democracy which the people of Britain, and indeed Rochdale, will understand and appreciate".
The policy announcement follows a Freedom of Information request by Unison, which revealed that some hospitals were charging staff, including nurses, almost £100 a month to park.
Labour say the plans would cost £162m, to be paid for by increasing Insurance Premium Tax on holders of private insurance from the current level of 12%, up to 20%.
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"Private medical insurance and cash plans cover around four million people in the United Kingdom from all walks of life".
"Extortionate parking costs are bad enough, but NHS staff are also being hit with huge fines, or having to nip out every hour to feed the meter".
"There are very few other public servants who have to pay for the privilege of parking".
"But expecting distraught families and underpaid staff to make up the difference through extortionate parking charges is not the answer".
A party source said that as with Labour's recent pledge to levy Value-Added Tax on private school fees to fund free school meals, it was "a policy for the many not the few - the many will benefit".
There will be one-on-one interviews with party leaders conducted by Andrew Neil throughout the campaign and a series of debates between leaders in Wales, Scotland and Northern Ireland. It will give them extra money in really tough times.
"Recent changes to the discount rate have cost the NHS over a billion pounds a year, roughly ten times the revenue raised through hospital auto parking charges".