Philip Hammond is proposing a “revolutionary” budget next month that will make “a big offer to the nation” on housing, tax and borrowing to try to save his job and prop up Theresa May after her party conference disaster.

Plans for a “safety first” budget have been abandoned after ministers concluded this was the “last chance” this year to “reset” public views of the government. The chancellor has asked his cabinet colleagues to come up with “bold” solutions and is prepared to consider easing austerity to boost housebuilding.

No 10 has asked for ideas to tackle “intergenerational fairness” after young people flocked to Labour at the last election. That has led Hammond to investigate the possibility of offering lower tax rates for young people, which