The Evangelical Alliance has called for a "fair and commonsense" approach to the gay marriage consultation, following the Cabinet reshuffle this week.

Among the key moves in what the papers described as a shift towards the right for the coalition government, were former employment minister Chris Grayling replacing Ken Clarke as justice secretary, and Baroness Warsi being removed from her role as Conservative Party co-chairman.

Other moves saw Justine Greening move to the Department for International Development and Owen Paterson to environment secretary.

But the Alliance feels greater clarity is needed over who is responsible for the consultation on gay marriage.

Dr Don Horrocks, head of public affairs, said: "In the government reshuffle, the minister responsible for the consultation on gay marriage, Lynne Featherstone, was moved from the Government Equality Office and replaced by the Conservative MP for Maidstone, Helen Grant, who will report to Maria Miller, the new secretary of state in the Department for Culture, Olympics, Media and Sport – instead of Theresa May in the Home Office.

"Somewhat confusingly, Helen Grant appears to have been made a justice minister in the Ministry of Justice but with a broader role across government as parliamentary undersecretary of state for women and equalities.

"She will be responsible for the government's response to the gay marriage consultation and for taking forward any consequent legislative proposals.

"We pray that she will adopt a fair and commonsense rather than the previous crusading approach to this highly controversial issue and that her record of commitment to marriage and the family will help her effectively protect marriage as we know it."

Elsewhere, Alliance member organisation Tearfund urged the government to stick to its commitment to those living in poverty.

Rosanne White, Tearfund's parliamentary officer, said: "The departing secretary of state for international development, Andrew Mitchell, has been energetic in his leadership, championing the cause of the world's poorest people in the face of strident opposition. But with the clamour that comes with a change in government, whether this change is intended to set public policy off on a new trajectory or to step up its implementation, these commitments must not be drowned out by short term political point-scoring or in appeasing the concerns of staunch party members. Let's hope that Justine Greening has the bottle to stand her ground."

Loretta Minghella, director of Christian Aid, also urged the government not to change its direction concerning the world's poor, praising Andrew Mitchell's "determination and courage".

She said:"We have been and remain impatient to see the government go further, especially in helping to end aid dependency. Aid alone will never end poverty, so we'd like to see DFID implement a credible exit strategy from aid.

"That would help poor countries generate their own resources, not least through more successful tax collection, including action against tax-dodging multinationals. This is what we will be pushing DFID on, in the months and years to come."