A Conservative minister said to have concerns about plans to open new grammar schools has resigned.

Lord Jim O’Neill, the former treasury minister who was appointed by George Osborne to steer the government’s northern powerhouse policy, also intends to move to the non-partisan cross benches in the House of Lords.

The former Goldman Sachs chair told the prime minister he considered that a key part of his role in government – achieving a UN agreement on antimicrobial resistance – had “come to its natural end”, but he is also said to be “annoyed” by Theresa May’s plan for new grammar schools.

The Financial Times reports that O’Neill is a board member of the Sutton Trust, which has criticised plans to increase selection in England, and also chairs the Shine Trust, which helps disadvantaged children and teenagers.

The prime minister Theresa May is already facing opposition to her proposals from within her party, but O’Neill’s decision to stand down could represent the first resignation linked to the grammar schools policy.