Employment is increasing at more than twice the rate of the wider UK economy, currently at 1.8 million jobs.
Creative England CEO Caroline Norbury called the employment and export figures "great news" but warned the sector "can't be complacent".
She said the workforce should "truly reflect the diversity of the UK".
Those from a BAME background working in the creative sector is now at 11% - in line with the rest of UK industry - but there is a gender imbalance, with women making up 36.7% of the workforce, compared to the national average 47.2%.
The report also found that 92% of jobs in the sector were done by people in "more advantaged socio-economic groups".
DCMS said that as many of the industries' jobs were classed as highly-skilled, that automatically propelled the people doing them into the higher group.
But Norbury told the BBC it was definitely harder for those from less advantaged backgrounds to gain entry to the creative industries.
"It's incredibly difficult to get a foothold in an awful lot of the creative sector, unless you've got family and friends working there already or can support yourself financially, because so many of the entrants coming into the industry may have to work for free initially."
Norbury added: "I don't think there's an active discrimination by the industry but the way the industry works, you need to have access to networks and if you don't know the ways of navigating that landscape, it's not enough sometimes that you have the talent.
"Generally as an industry we're all a bit full of ourselves and we expect people to find us - and some people can - but a lot of people actually wouldn't know how to. So I think there's a real responsibility on us to make ourselves accessible and to go out and find people."
Culture secretary John Whittingdale said: "These latest figures demonstrate how the UK's creative industries continue to be one of our great success stories.
He called it a "fantastic sector", adding: "Our films, music and other artists are celebrated around the world and this Government is determined to do what we can to ensure our creative industries continue to grow."
Jobs within the sector increased by 5.5% between 2013 and 2014, compared to the national 2.1% rise in employment, and have now increased by 13.7% since 2011.
The number of BAME workers in the creative industries increased by 8% between 2013 and 2014 and has risen by 34.3% since 2011.
The figures also show that exports from the creative sector are outperforming the rest of economy by almost 15%, increasing by 34.2% to around £4.5bn between 2009 and 2013.
"It's very interesting that the creative sector is becoming such a driver," said Norbury, "and yet people are still so sceptical about it.
"How does that knowledge then feed into our education system, our industrial policy and so on? There's a little bit of a mismatch between the facts and the common parlance. The fuel for that [success] is a really great arts curriculum."
Article source: BBC Entertainment & Arts