The umbrella body's manifesto for next month's general election says greater funding for charities, deprived communities and local councils is needed to create a better, more inclusive economy.
The Directory of Social Change and the charity leaders body Acevo have also published their pre-election wishlists
The manifesto also says the UK Shared Prosperity Fund, the replacement for EU funding to the UK, must deliver "a comparable level of investment" to that already provided. Local government funding should be increased to help ease the strain on public services, according to the manifesto, with councils having seen a real-terms cut of 50% since 2010.
A community wealth fund using some of the billions of pounds of dormant assets identified by a recent independent commission should be set up, the manifesto says, to invest in deprived communities. A resilient communities fund should also be formed to help charities in the event of a no-deal Brexit, the manifesto says, and new community spaces should be created.
EU standards should be upheld on EU citizens' rights, environmental regulations and workers' rights, and a statutory duty for volunteering should be introduced, the manifesto says.
Other proposals include implementing the recommendations of the Charity Tax Commission, involving charities more in policymaking, reforming the lobbying act, providing clarity on anti-advocacy clauses and greater scrutiny of how the Charity Commission's chair is appointed.
The government should also strengthen its commitment to social value and take decisions in the interest of future generations, according to the NCVO's manifesto. The Directory of Social Change has also called for politicians to enact five policies to help the charity sector.
In a blog posted on the DSC's website, Jay Kennedy, director of policy and research for the training and publishing charity, renewed calls for the immediate repayment of £425m in National Lottery money that was taken in 2007 to finance the London Olympics in 2012. Kennedy also wants the Charity Commission to be prevented from charging charities to fund its services, and instead provide funding for the regulator from general taxation.
Reforming the lobbying act to implement the reforms proposed in the Hodgson review, restoring grant funding and a community wealth fund are also among Kennedy's proposals. The leaders' body Acevo has also called on politicians to work in partnership with the charity sector and to show leadership and creativity in addressing the country's problems.
"MPs need research from both grass-roots, national and international charities in order to be able to govern effectively," Acevo's manifesto says. "Civil society organisations need politicians to build the structures and rules that will help them achieve long-term, sustainable change.
"The new parliament needs to move beyond transactional relationships with civil society, instead working to build understanding, trust and respect, to inform better decision-making and to ensure people can access the support and opportunities they need."
You can read the manifesto Here
Read: Third Sector - NCVO calls on the next government to do more to engage with civil society.