Kerry McCarthy, Labour MP for Bristol, was speaking at a Fabian Society conference on green spaces in London on 18 April, a week after the parkrun controversy made national headlines.
Stoke Gifford Parish Council raised the hackles of joggers across the country after it decided to ask for a financial contribution from the parkrun held in a parish park each Saturday morning.
The timed 5km runs, participation for which has been free until now, are regularly held in Little Stoke Park near Bristol, with around 300 runners attending. They are billed as a way of getting everyone in the community to feel comfortable exercising and participating in community activities by removing barriers to participation, including any sort of charge.
The run's organisers have warned that a fee would go against the ethos of parkrun and make the event untenable. But Stoke Gifford said it is facing a large repair bill for the park and wants some financial contribution from the group in light of the "wear and tear" the runners cause to paths and other parts of the park. It is believed to be the first council in the world to introduce a charge for parkrun. At the time of going to press nearly 60,000 people had signed a petition calling for the event to remain free.
Dave Morris, London chair of the National Federation of Parks & Green Spaces, said the group is "greatly heartened" by the reaction to the council's decision but pointed out that the real issue is that councils are "desperate" for funding.
Graham Evans MP, chair of the All-Party Parliamentary Group for Running, said: "Parkruns provide an invaluable way of utilising public spaces and getting the whole community involved - young and old - in physical activity, which we all know is massively important for our health and well-being.
"I have written to this parish council with some suggestions of how they may like to fundraise towards the maintenance of the park if they have found that the costs are above and beyond that raised by council tax contributions."
Parkrun founder Paul Sinton-Hewitt said in a letter to supporters that the group is "extremely disappointed" with the council's decision to introduce charges. Legal avenues to challenge the decision are now being investigated.
Speaking at the Fabian Society conference, McCarthy said there is a "worrying agenda" in Government of making green spaces pay for themselves, pointing to the announcement earlier this year that national parks would be encouraged to find more ways of raising their own income.
The "absolute public outcry" that arose after the parkrun decision was publicised suggests that the Government's approach will not work, said McCarthy. Parkrun is "an emotive issue", she added.
"It's easy to say that parks should be run as a public good but when budgets are tight there's a discussion that has to be had. It needs to be a local decision, whether to open up the park with cafes, for example, or maintain it as a free space."
Lydia Ragoonanan, who headed up Rethinking Parks, said the events around the Stoke Gifford parkrun had "captured the public's imagination". She added: "We need to recognise the really tough position councils are in...rather than just berating them. We need to give them new options."