In a letter to David Cameron and William Hague, CSW calls for pressure to be put on President Susilo Bambang Yudhoyono to protect the rights of religious minorities and defend the rule of law.
In particular, the organisation raises concerns over the forced closure of churches in Indonesia, including churches that have secured legal permission.
The Jakarta Globe newspaper reported last week that nine churches and six Buddhist temples had been closed down as a result of intense pressure from local Islamist groups.
The GKI Yasmin church in Bogor and HKBP Filadelfia church in Bekasi were both closed by the local mayor amid pressure from extremists, despite the courts ruling that the churches should remain open.
"This is a rule of law issue, not simply a religious freedom issue," the letter states.
The organisation further warns that Indonesian democracy could be undermined if human rights violations in West Papua are not addressed.
It wants to see the Indonesian president follow the recommendations of the Papua Road Map and enter into dialogue with the Papuans.
Andrew Johnston, CSW’s Advocacy Director, said the president's visit was an important opportunity to deliver clear messages about human rights.
He said: "Indonesia’s remarkable transition from authoritarianism to democracy over the past decade and its tradition of pluralism and religious harmony deserve to be recognised, but these achievements are being increasingly undermined by rising Islamist extremism, violence against religious minorities, discriminatory laws which are open to abuse, particularly the blasphemy laws, regulations governing the construction of places of worship, regulations relating to the Ahmadiyyah Muslim community and the abuses perpetrated by the Indonesian military in West Papua.
"During this visit, the British Government should raise these concerns as a matter of priority, and urge the President to take action to protect and promote human rights and curb religious extremism and violence.”