A Labour government would be prepared to introduce the "nuclear option" of quotas for female and black and ethnic minority judges to avoid a 100-year wait to achieve a judiciary reflecting the composition of the population.

The shadow justice secretary, Sadiq Khan, said reform had slowed to a snail's pace and called for radical thinking to ensure judges were selected from beyond the "male, white and Oxbridge" world.

Khan, who accused the government of harming progress towards a diverse judiciary with swingeing cuts to the legal aid budget, has appointed Sir Geoffrey Bindman QC and Karon Monaghan QC, two of Britain's leading progressive lawyers, to "think big" on how to achieve a balanced judiciary. "Nothing is off the table," he said of the remit.

Khan said: "This is such a big issue that I don't want Geoffrey and Karon to be afraid to recommend anything."

Bindman and Monaghan are expected to focus on practical proposals such as introducing a mentoring and talent-spotting scheme to identify talented women and black and minority ethnic (BME) legal figures early on in their career.

But the two QCs will be free to recommend the introduction of positive discrimination along the lines suggested in a speech this year by Lady Hale, the only woman who sits in the supreme court.

Khan believes it is important not to rule out introducing quotas for women and BAME judges as a last resort. "Let us see what Geoffrey and Karon come up with," one Labour source said. "You would want to keep the option of more radical measures like quotas on the table as a last resort. It would be the nuclear option."

The introduction of quotas would be controversial because they were rejected by the House of Lords, which in a report in 2012 laid bare the poor representation in the judiciary of women and BME candidates. The committee heard evidence from the association of women solicitors that quotas would send out a message that a candidate had been chosen solely on the basis of gender or race.

But the Lords committee did call for non-mandatory targets after five years if little progress had been made towards a more diverse judiciary. It said 22.3% of judges were women – the fourth lowest rate in Europe – while 5.1% had BME backgrounds.

Khan said radical action was needed because insufficient progress had been made in the two years since the committee's report was published.

He said: "If we just sit back and do nothing, it'll take a century for our judges and magistrates to reflect wider society. I'm not prepared to sit by and let things move along at a snail's pace.

"Too many judges are still drawn from too narrow a background. An overwhelming number are male, white and Oxbridge. People's differing backgrounds and experiences bring different and rich perspectives that improve their decision-making as judges. If we achieve this it's my view that we'll see a dramatic impact on the public confidence in our justice system."

Khan, a lawyer, who first entered parliament in 2005, asked for radical thinking after outspoken intervention by two supreme court justices. Lady Hale said in February that positive discrimination might be needed to overcome the gender imbalance among senior judges. In the Kuttan Menon memorial lecture, sponsored by Bindmans, she said just 15.5% of high court judges were women and 4.5% were from BME backgrounds. Only 10.5% of judges in the court of appeal were women and there were no BME members.

Lord Sumption, Hale's fellow supreme court justice, warned that it would take another 50 years to achieve a balanced judiciary. Alan Paterson, a professor at Strathclyde University law school, has said it could even take a century.

Sumption called for a public debate about the "hitherto unmentionable subject of positive discrimination" after the Lords report found that, on current trends, the judiciary would not achieve a gender balance until 2040. It would not achieve an ethnic balance until 2035.

A Labour source said: "At the moment we have a very passive process. People apply and are appointed. This programme would help advise potential candidates on the areas they would need to work in to increase their chances of becoming a judge."

Bindman and Monaghan will also examine barriers to joining the judiciary, . Circuit judges are expected to travel and spend a lot of time away from home, a factor that rules out this option for many women. The two QCs will also look atother routes to joining the UK judiciary.

Meanwhile, the justice secretary, Chris Grayling, has said foreigners should be prevented from using legal aid to fight British court cases in order to stop the justice system being brought into disrepute.

In an article in the Telegraph, he accuses pressure groups and law firms of profiting from legal cases aimed at blocking government decisions. Grayling, who is battling members of the legal profession over attempts to cut spending on legal aid and toughen rules on judicial review, said a small number of firms and pressure groups "make a healthy living by finding more and more varied ways to challenge government in court – and getting you to pay the bill".

He also said that society was too legalistic, and "where the system can be, and is exploited inappropriately by pressure groups with a political point to make, and a minority of lawyers who make money out of creating opportunities to attack government, Parliament and the decisions they make."

He highlighted cases brought by Public Interest Lawyers, who acted for Iraqis, but whose legal aid was paid for in the UK.