Dernbach was born in Johannesburg, South Africa to a South African father and an Italian mother and has used an Italian passport. He moved with his family to England in 2000 when he was 14. In South Africa, his preferred sport was rugby union, but he began to develop as a cricketer in England. After bowling at an under-15s net session at Surrey, he quickly moved through the age groups.

Although born in South Africa, after his first call-up to the England squad, he stated that "I don't owe anything to South Africa. I was just born there, did a bit of schooling there, my whole cricket career has been based in the UK, and UK is my home. I want to give everything I can to England cricket, that's the country I love and that's the country that has given me everything I have now."

In 2013, Dernbach became the first UK-based athlete to pose for a PETA "Ink Not Mink" advertisement, showing off his arm and chest tattoos on behalf of the anti-fur campaign.

His consistency and regular wicket-taking for Surrey was rewarded with a place on the 2011 England Lions tour to the West Indies, before a late call-up to England’s 2011 World Cup squad made him the first Surrey youth academy graduate to secure recognition at this level. He continued to perform well for Surrey whenever available. His 2011 season was capped with a Man of the Match performance in the CB40 Final, where his 4/30 helped lift Surrey to victory.

Dernbach was effective in Surrey’s successful T20 campaign in 2013, and was the side's leading wicket taker with 18 wickets (at an average of 16.44) as Surrey reached the Finals Day at Edgbaston for the first time since 2006.

In 2010, Dernbach was selected for the England Performance Programme tour of Australia and subsequent England Lions tour of the West Indies where they participated in the domestic Regional Four Day Competition. In the latter, he took 19 wickets at an average of 15.63, making him the leading English bowler.

He was called up to the senior team as a replacement for Ajmal Shahzad for the knock out stages of the 2011 Cricket World Cup^[8] but was not picked to play.

At the beginning of the English season, he was then picked for the Lions to face the touring Sri Lankans. He took 9 wickets in the match, although the Lions ultimately lost the match.^[9] However his performance saw him included in the senior squad for the second Test after an injury to James Anderson. He had to wait until the limited overs games to make his debut; taking 1–18