A Downing Street source confirmed that the review would examine allegations that the Muslim Brotherhood was behind the murder of three tourists on a bus in Egypt in February and that it planned extremist activities from Britain.

The source said: "The prime minister has ordered a review to get a better understanding of the Muslim Brotherhood and its values – and look into its alleged links to extremism."

The No 10 source confirmed a report in the Times that the investigation is being launched as the prime minister faces pressure to follow the example of Egypt and Saudi Arabia, which claim that the Muslim Brotherhood uses London as a crucial center for its activities, to ban the group.

The Times reported that MI6, Britain's overseas intelligence agency, would examine claims that the Muslim Brotherhood was behind the bus attack in Egypt. MI5 will assess how many leaders have been based in Britain after last year's coup in Egypt in which Mohamed Morsi, the Muslim Brotherhood president, was ousted.

The regime of Abdel Fattah el-Sisi, the head of the Egyptian armed forces who played a leading role in the overthrow of Morsi last year, has placed the former president on jail where he awaits trial for treason. Morsi was the candidate for the Muslim Brotherhood's Freedom and Justice party for the 2012 presidential elections in Egypt.

Cameron ordered the investigation after it was concluded that Whitehall has insufficient intelligence about the Muslim Brotherhood's activities in Britain and in Egypt.

Downing Street has asked Sir John Jenkins, the British ambassador to Saudi Arabia to draw up a report on the Muslim Brotherhood's "philosophy and values and alleged connections with extremism and violence".

The Muslim Brotherhood, which was founded in Egypt in 1928, was branded a terrorist group by the Egyptian authorities last year.

NJF/NJF