Labour leader Jeremy Corbyn focused on housing costs as he took on Theresa May in the first Prime Minister's Questions since the summer recess.

He said home-ownership was just a "dream" for many people and that housing benefit was being paid to landlords renting out "unsafe homes".

Mrs May said tough measures were in place including money for councils to carry out more inspections.

She also said women's refuges could be exempt from a housing benefit cap.

Live: PMQs and reaction

After Mr Corbyn warned of "devastating" refuge closures when payments are capped at the same level as in the private rented sector, the PM told the Commons the government was "working on exempting refuges from the cap".

"We are listening to these problems and we are responding to them," she added.

Leadership jibes

Labour is in the middle of a leadership contest, and before PMQs Mr Corbyn's rival, Owen Smith, urged him to target the EU negotiations with his questions.

But Mr Corbyn chose instead to quiz the PM on housing, saying house-building had fallen under the Tories and that council houses sold off were not being replaced.

The PM said this was not the case, adding that Mr Corbyn wanted a society where there were no private landlords and with the government "owning everything".

"We want opportunity for everyone," she said, adding that this was a "big difference between him and me".

She included jokes - including about Mr Corbyn's row with Virgin Trains - in her answers, with the Labour leader ignoring the jibes as he responded.

Mrs May was also asked twice by SNP Westminster leader Angus Robertson whether she wanted the UK to remain in the EU single market after Brexit, responding that she would not give a running commentary on the negotiations.