David Cameron hailed the latest stage in the "great fight" against discrimination as employers including HSBC and the BBC introduced measures to curb potential bias against candidates with "ethnic sounding names".

The Prime Minister said ending discrimination would help make the best use of the talent available in Britain, benefiting companies and the country as he hosted a meeting at Downing Street to discuss the issue.

Number 10 said Deloitte, Virgin Money and KPMG would also begin selecting for interview for graduate and apprentice roles without knowing names.

Mr Cameron thanked the employers for taking action and stressed it was more than just a "symbolic" step as he hosted the event in Number 10.

The civil service - which already employs the practice for around half of jobs - will extend it to all but the highest tier of mandarins, meaning around 99% of positions will be recruited.

It will be made the default for all positions advertised through NHS Jobs and health service apprenticeships delivered through the National Careers Service.

The Local Government Association has committed to encouraging town halls to take it up - as well as applying it to its own recruitment.

Mr Cameron has introduced it for Conservative Party appointments.

The Prime Minister told the gathering of business leaders at Number 10: "I know this is only one issue, it doesn't solve the problem on its own, but I think it is not just symbolic, I think it makes a real difference. So thank you very much for doing that."

Mr Cameron, who railed against employment discrimination in his party conference speech, explained why he was maintaining his focus on the issue.

"It is just worth pausing and thinking about why this matters so much. To me, why it matters is, obviously, there is a great fight against discrimination which we haven't completed in our country and we must complete.

"As I said in my party conference speech, if you don't deal with the issue of discrimination, you can never have true opportunity - which is what we all want to see."

"We will never be as effective a country as we could be, companies will never be as effective as they can be, government will never be as effective as it could be - the army, courts, politics itself - will never be as effective as it could be unless we use the talent of our country to its very best effect."

He added that tackling discrimination is "not just about seeking after justice and something that we ought to do, it is something we should actively want to do in order to maximise the ability of our companies, our country, to be everything that they can".

The PM said in his conference speech that having a "white-sounding" name made you nearly twice as likely to get a call-back from an application than someone equally qualified.

He said it was "disgraceful" in 21st century Britain that one black graduate had only got interviews after changing her name to Elizabeth.

It is hoped the "name blind" practice will be spread further across the private sector by being incorporated into training courses run by the Chartered Institute of Personnel and Development (CIPD).

Deloitte chief executive David Sproul said it would also use "school and university-blind" interviews in a bid to end "unconscious bias".

"We want to show that everyone can thrive, develop and succeed in our firm based on their talent, regardless of ethnicity, gender, sexual orientation, or any other dimension that can be used to differentiate people from one another," he said.

Civil Service chief executive John Manzoni said: "It's vital that the Civil Service takes a lead on this, and I'm confident that this important step will help us build an organisation that is even more talented, diverse and effective than it is today."

Participants in the Downing Street event included Deloitte's managing director David Barnes; HSBC's head of HR Tanuj Kapilashrami, Civil Service chief executive John Manzoni, NHS England chief Simon Stevens, KPMG's head of corporate affairs Marianne Fallon and BBC strategy director James Purnell.