Graham Brady, head of the influential 1922 committee of MPs, which Theresa May has been told she must now listen to, has said he believes the party will now look at a “modest” pilot of grammar schools.

Over-turning the ban on selective schools was a key pledge in the Conservative manifesto, however the party’s failure to secure a working majority means it will be difficult for all promises to be fulfilled.

In the Queen’s Speech, due as parliament returns, the government must lay out its plans for government.

The controversial nature of grammar schools, with several Conservative MPs having publicly stated they will vote against any laws trying to resurrect them, would be difficult for the party to pass.

Asked on BBC’s Sunday Politics about the speech, Brady admitted the policies included in it would need to be “slimmed down” as there was “no point in sailing ahead with items in the manifesto that we won’t get through parliament.”

Pressed on whether grammar schools would be dropped he said he would be “upset” if no “progress” was made on the policy but that a “rather modest sort of pilot” might be an alternative.

He said: “If we can’t get things through parliament, then we can’t do them.

“But I would certainly suggest that we could look, for instance, at a rather modest sort of pilot looking at opening some state grammar schools in urban areas, particularly those where education at the moment is not offering great opportunities to people from lower income backgrounds.”

Brady added that he believed the support would also have support from “friends on the Labour backbenches” who he said had quiet support for an approach targeting such areas.