In an open letter to the next UK government, Dan Corry, chief executive of NPC, says that moving the OCS to the Cabinet Office would ensure civil society had a voice "at the heart of government" and could make contributions to policy decisions.
The OCS was part of the Cabinet Office until last year, when it was moved to the Department for Culture, Media and Sport.
The decision to move the OCS was viewed as a demotion and a backward step for charities by many sector representatives at the time.
The open letter includes a call to make the Charity Commission ensure that reporting on an organisation’s impact is a "formal responsibility of equal importance to its financial position".
It says: "The current focus of regulation remains almost purely on financial stability and organisational survival. If charities and the wider civil society sector are to work in new ways to deliver greater impact, regulation must encourage a greater focus on the impact delivered.
"Enacting this recommendation would ensure trustees pay greater heed to the mission of the organisation and the difference they are trying to make, rather than just how to keep the show on the road."
The letter says the government should ensure grants are funnelled to organisations that can demonstrate their impact, and require grant-making trusts to publish the reasoning behind their payout ratios.
The Public Services (Social Value) Act should also be reconsidered in the light of the vote to leave the EU to ensure public contracts are awarded based on the impact delivered rather than what can be delivered for the cheapest amount possible, the letter says.
A targeted social infrastructure fund using some of the £2bn discovered by the Dormant Assets Commission, a review of the tax breaks received by charities and an extension of the Ministry of Justice’s Data Lab model to health, employment and education are also recommended by the letter.