The Green party will on Friday call for the minimum wage to be raised to £10 an hour within the next parliament, in a move that appears to be aimed at stealing support from Labour.

On the first day of its annual conference in Birmingham, Natalie Bennett, the party leader, will call for the minimum wage of £6.31 to be immediately raised to the level of the living wage, which is £7.65 for everywhere except London, where it is £8.80.

In a new manifesto pledge, she will call for the different levels of minimum wage for young people and adults to be abolished, leading to a £10 minimum wage for all by 2020. The Greens said the rate should then be linked to living costs to ensure that it rises alongside inflation.

Raising the minimum wage to living wage levels would benefit an estimated 5.2 million people – 17% of the working population – and bring in a "fairer society where fewer workers are trapped in poverty pay conditions", the party said.

Pitching the Greens as the only anti-austerity party, Bennett will say there is very little between the policies of the Conservatives, Labour and Liberal Democrats.

Bennett told the Guardian: "We need to offer people hope for the future – a living wage, secure employment and no more zero-hours contracts."

Like Ukip, Bennett said the Greens were also a party that was "not offering people business as usual". "Under our plan no one would be paid less than £10 an hour in 2020," she said. "It is a scandal that under the coalition government the number of workers earning less than the living wage has risen by a staggering 50%. It makes a mockery of David Cameron's 2010 statement that a living wage is 'an idea whose time has come'."

"The fact that the Green party are consistently polling at some of our best numbers since 1989 goes to show that our message of the need to reshape our politics and economy to work for the common good is really hitting home.

"It is our policies such as making the minimum wage a living wage, a wealth tax on the top 1%, re-nationalising our railways and having a publicly owned and run NHS that are both encouraging people to join as members and vote Green in growing numbers."

The Green party has not managed to replicate the surge of Ukip but it came ahead of the Lib Dems in the European elections. The party, which is targeting disillusioned ex-Lib Dems as well as traditional Labour voters, had support of about 6% in a poll of polls last month, while the Lib Dems were on 9%.

Another key focus of the party conference will be on protecting the NHS from privatisation. Bennett argued that the Conservatives and Lib Dems have been responsible for a creeping sell-off of the NHS under the coalition, while Labour started the process under the last government.

Labour has promised a higher minimum wage linked to average earnings but has not put a not figure on how much it should be. Ed Miliband has also promised to tackle abuse of zero-hour contracts by forcing employers to put staff on permanent hours after a certain time but he has not pledged to outlaw them completely.

Labour sources argued a vote for the Greens was a vote for higher taxes, new restrictions on drivers, higher benefits for people who choose not to work and soft laws on drugs.