Jeremy Corbyn risked being accused of missing a political open goal during this week's Prime Minister's Questions (PMQs)after the Labour leader decided to grill the Conservative premier over the issue of housing.

The left-winger's decision to cross-examine May over the subject meant he failed to mention the government's Brexit plans or yesterday's embarrassing new grammar schools gaffe, which saw the leak of a Department for Education memo thanks to a long-lens camera on Downing Street.

"The average house price in Britain is now £215,000, over eight times the average wage," Corbyn said at the first PMQs after the summer recess.

"The average price of a first time buyer's home has risen by 12% in the past year. Isn't the dream of home ownership for many people just that, a dream?"

May replied: "Of course, it is important for us to look at helping people get their first step on the housing ladder. That's why I'm pleased that house building has been up under a Conservative government compared to a Labour government.

"But we're not complacent that's why we will be doing more to see more houses built under this Conservative government and also to continue to provide support for people to make sure that they have that financial support that helps them to own their own home."

Corbyn then used four more of his six permitted questions to question May over housing, finally turning to issue of women's refuges across the UK. The prime minister revealed that her government was working to exclude the shelters from the housing benefit cap.

The comments come after the charity Women's Aid warned 67% of the domestic abuse shelters would face closure if they were not given an exemption.

Smith unimpressed by Corbyn's performance

Owen Smith, the Labour leadership challenger, published an open letter to Corbyn ahead of this week's PMQs. "You didn't even ask her about the EU, even though Brexit was and is the biggest challenge facing her government, and the reason for David Cameron's resignation and her elevation to Downing Street," he said.

"Perhaps the same reticence about standing up for Britain's place in the EU which led you to campaign so ineffectively for Remain also puts you off exposing the weaknesses and contradictions in the Government's position – but continuing to fail to take Theresa May on over Brexit would be a dereliction of duty.

"This week, you can make up for it – especially with the collapse of several key planks of the Leave campaign, the splits emerging in the Cabinet, the serious concerns emerging among our international allies at the G20 summit and the inadequacy of Theresa May's vapid 'Brexit means Brexit' formulation which have all become apparent in the last week. Last week's Chequers 'Brexit Brainstorm' provides rich material too."

Corbyn seemed to avoid the former shadow work and pensions secretary's advice.