Labour will work with back-bench Conservatives to oppose government plans to turn all schools into academies, Lucy Powell has confirmed.

The shadow education secretary said she was willing to work with anybody to “win the arguments” against the proposals set out in the government’s white paper, including Conservative MPs with concerns about the academies plan.

The Conservative backbench 1922 Committee chair Graham Brady is the latest high-profile party figure to come out against the plans. His intervention comes after Melinda Tilley, Oxfordshire’s cabinet member for education, joined the leaders of several teaching unions and politicians including Ms Powell in signing a letter to the Telegraph calling for a re-think.

Schools minister Nick Gibb this morning defended the government’s plan to have every state school converted into an academy by 2022, when he was interviewed at the Association of Teachers and Lecturers annual conference, saying “it is about making sure we don’t have two systems of oversight”.

But Ms Powell, who received a far less frosty welcome at the event in Liverpool than Mr Gibb, told journalists after her appearance that it was becoming “increasingly clear” how few people supported the plans, and said a “growing alliance” against academisation may force the government to “look again”.

Repeating her preference for a strengthened oversight role for councils, Ms Powell admitted the parliamentary maths meant opponents would have to focus on “winning the arguments, rather than winning votes in Parliament”.

Legislation on the forced academisation of schools is yet to be introduced in Parliament and although the Conservatives have only a slim majority in the House of Commons, a large number of the party’s MPs would have to rebel to defeat it, because Scottish National Party MPs are unlikely to vote on an issue affecting just England.

ATL members are expected to vote tomorrow on possible strike action over the impact on pay and conditions of the white paper plans. The National Union of Teachers has already committed to a ballot of members.