The Heritage Lottery Fund (HLF) said it wanted to "help applicants in tough times" and was responding "to economic challenges facing potential and current applicants".
Chief executive Carole Souter said: "There will be more money on offer for applicants who are finding it hard to raise funds elsewhere.
"As well as helping new applicants, any project already underway facing difficulties from the economic conditions should contact their case officer. We want to help."
Match-funding for requests of more than £1m have been cut from 25 per cent of the project costs to 10 per cent, and "HLF will be able to make up all of the remainder".
For grant requests of less than £1m, the minimum match-funding requirement has been reduced from 10 to five per cent of total costs.
Similar changes have been made for joint programmes, such as Parks for People, run with the Big Lottery Fund, with the same percentage drops for big and small requests.
HLF head of landscape and natural heritage Drew Bennellick said of the UK's 27,000 parks, around 2,000-3,000 were historic and the HLF had funded 500 of them - around 20 per cent.
"There's a huge amount to do before we have dealt with all of those parks," he explained. "Heritage is very much driven by the community, which must demonstrate heritage value."
Other changes include allowing applicants to count management and upkeep plans, which must accompany larger requests, as a contribution to match-funding.
HLF will also consider pleas for short-term revenue funding from past grant holders where the downturn puts the achievements of previously-funded projects at risk.
This is the second recent change from the HLF. Three months ago it offered a raft of measures on large grants and application deadlines.
Souter said: "There will be more money on offer for applicants who are finding it hard to raise funds elsewhere and new ways of protecting HLF's past investment.
She added: "We are also looking at other ways to help with challenges to the heritage sector after the spending review."