"One day, I want to hear that title Prime Minister followed by a British-Asian name," he said in his speech at the annual GG2 Leadership Awards here on Wednesday night.
"Just not immediately, if that's ok," he added on a lighter note in reference to the upcoming general election in Britain in May 2015.
"What makes Britain a success is that every community has a hand in it ... but frankly it is still not enough. In Britain today there are still too few people from ethnic minorities in top positions," he said.
"The absence is glaring in boardrooms, chambers of Houses of Parliament, on football manager's benches, on high court judges benches and in our fighter jets and naval ships. And, I am clear, this has to change," he added before presenting the GG2 Man of the Year and Woman of the Year Awards for 2014.
The Man of the Year award went to Indian-origin businessman Rami Ranger, CEO of Sun Mark Limited, who was described as a "brilliant entrepreneur" by the PM for his contribution to the British economy.
Woman of the Year was named as Dame Asha Khemka, principal of West Nottinghamshire College, for her work in the field of education.
"I am truly humbled by this award. I often say, India made me and Britain enabled me. My heart lies in India and my soul in Britain," she said in her acceptance speech.
The event also marked the launch of the 'Power 101 Britain's Most Influential Asians 2015' list, which this year is topped by UK secretary of state for culture, media and sports Sajid Javid - the first Asian to be promoted to the UK Cabinet.
Born to an Indian father and Pakistani mother, Javid dedicated his honour to his parents' memory.
Others in the top 5 included Pakistani teenage campaigner Malala Yousafzai, down to No 2 from top spot last year, Indian-origin Labour MP Keith Vaz at 3, Indian steel tycoon Lakshmi N Mittal at No 4 and Hinduja brothers at No 5.
NRI industrialist Lord Swraj Paul and son Angad, chairman and CEO of Caparo Group of industries, curry king Lord Gulam Noon and Deutsche Bank's Indian-origin CEO Anshu Jain also find their place in the Power 101.
The annual event is organised by the Asian Media and Marketing Group, publishers of 'Garvi Gujarat' newspaper from where the name GG2 is derived.