Some of Britain's top landowners, celebrities and the offspring of senior Establishment figures have embraced the strict tenets of the Muslim faith.

The trend is being encouraged by Muslim leaders who are convinced that the conversion of prominent society figures will help protect a community stigmatised by terrorism and fundamentalism.

Zaki Badawi, chairman of the Imams and Mosques Council, said: "The community has been unfairly targeted and these developments encourage it in a time of difficulty." Meanwhile, the Muslim Council of Britain has co-opted Joe Ahmed-Dobson, son of Frank Dobson, the former health secretary, to chair its regeneration committee.

The new study by Yahya (formerly Jonathan) Birt, son of Lord Birt, former director-general of the BBC, provides the first reliable data on the sensitive subject of the movement of Christians into Islam. He uses a breakdown of the latest census figures to conclude that there are now 14,200 white converts in Britain.

Speaking publicly for the first time about his faith this weekend, Birt, whose doctorate at Oxford University is on young British Muslims, argued that an inspirational figure, similar to the American convert Malcolm X for Afro-Caribbeans, would first have to emerge if the next stage, a mass conversion among white Britons, were to happen.

"You need great transitional figures to translate something alien (like Islam) into the vernacular," he said. "The image of Islam projected by political Islamic movements is not very attractive."

Initially, Birt said, he had no coherent reasons for converting, but: "In the longer term I think it was the overall profundity, balance and coherence and spirituality of the Muslim way of life which convinced me."

The faith has made inroads into the Establishment. It emerged this weekend that the great-granddaughter of a British prime minister has converted. Emma Clark, whose ancestor, the Liberal prime minister Herbert Asquith, took Britain into the first world war, said: "We're all the rage, I hope it's not a passing fashion."

Clark, who helped design an Islamic garden for the Prince of Wales at Highgrove, his Gloucestershire home, is now helping create a similar garden for a mosque in Woking, Surrey, on the site of a car park.

Many converts have been inspired by the writings of Charles Le Gai Eaton, a former Foreign Office diplomat. Eaton, author of Islam and the Destiny of Man, said: "I have received letters from people who are put off by the wishy-washy standards of contemporary Christianity and they are looking for a religion which does not compromise too much with the modern world."

Others have come to Islam through love or marriage. Kristiane Backer, a former girlfriend of the cricketer Imran Khan, said she was introduced to the religion through love but converted after her break-up. She has shrunk from speaking publicly about her religion before because of fears it might affect her work prospects.

"Imran sowed the seeds, but when (the relationship) finished (the faith) took on a momentum of its own," she said. Backer, who is drawn to Sufi mysticism, said white converts had to overcome prejudice both from those born into Islam and from non-believers.

"In the mosque women come up and say to me, 'You have hair showing: you must cover up completely.' I say, 'Mind your own hair, you're here to think about God'."

She has ditched the revealing wardrobe she had as an MTV presenter, but, equally, will not wear headscarves about town. "I don't show any legs or cleavage, or at least not together," she said.