In a speech at the East London Muslim Centre in Whitechapel, Lord Phillips said that sharia suffered from "widespread misunderstanding".
Lord Phillips said: "There is no reason why sharia principles, or any other religious code, should not be the basis for mediation or other forms of alternative dispute resolution.
"It must be recognised, however, that any sanctions for a failure to comply with the agreed terms of mediation would be drawn from the laws of England and Wales."
Severe physical punishments such as flogging, stoning and the cutting off of hands would not be acceptable, he said.
He added: "There can be no question of such courts sitting in this country, or such sanctions being applied here.
"So far as the law is concerned, those who live in this country are governed by English and Welsh law and subject to the jurisdiction of the English and Welsh courts."
'Misunderstood'
The Archbishop of Canterbury, Dr Rowan Williams, had been misunderstood when it was reported in February that he said British Muslims could be governed by sharia law, the judge said.
Dr Williams suggested that sharia could play a role in "aspects of marital law, the regulation of financial transactions and authorised structures of mediation and conflict resolution".
Lord Phillips said: "It was not very radical to advocate embracing sharia law in the context of family disputes, for example, and our system already goes a long way towards accommodating the archbishop's suggestion.
"It is possible in this country for those who are entering into a contractual agreement to agree that the agreement shall be governed by a law other than English law."
Inayat Bunglawala from the Muslim Council of Britain told BBC News that sharia law applied only to civil matters.
He said: "I think it's important to clarify that English common law already allows us to go to mediation to whichever third party we wish. "So that is why you have sharia council, that is why you have Jewish courts. It is a truly voluntary arrangement.
"There is no parallel legal system. This system cannot override English common law system at all."
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English common law already allows us to go to mediation to whichever third party we wish
Muslims on UK Sharia
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