Written by Gordon Rayner and Duncan Gardham
The majority of cases heard in the courts involve divorce or financial disputes, but one reported case involved a gang of Somali youths who were allowed to go free after paying compensation to a teenager they had stabbed.
Extremists were said to have used the spread of Sharia courts to justify calls for Islamic law to be adopted "wholesale" for Muslims living in Britain.
Anjem Choudary, a solicitor and former senior figure in the banned organisation Al Muhajiroun, said: "Some element of family law or social and economic law will not work. It has to be adopted wholesale. It will not happen tomorrow but it is inevitable because Sharia is superior and better for mankind."
Despite grave warnings from lawyers about the dangers of a dual legal system, criminal cases are already being dealt with by some of the unofficial courts. In 2006 an Islamic Council sitting in Woolwich, south-east London, heard the case of the Somali gang, who had been accused of stabbing another Somali teenager and were reportedly arrested by the police.
Aydarus Yusuf, a youth worker, told Radio 4's Law in Action programme the suspects were released on bail after the victim's family said the matter would be dealt with by the Islamic community. "All their uncles and fathers were there," said Yusuf.
"So they all put something towards that and apologised for the wrongdoing." The Metropolitan Police said it was unaware of the case, but admitted that officers sometimes did not proceed with assault cases if the victim decided not to press charges.
Yusuf told the programme he felt more bound by Sharia law than by the laws of his adopted country.