The group insists it remains an entirely peaceful organisation but is accused of being behind a wave of deadly attacks on the police and military.
Responsibility for a bomb attack on a tourist bus in the Sinai peninsula which killed three South Koreans from a church group and the Egyptian driver, is also among issues being examined.
The prime minister’s review is being led by Sir John Jenkins, Britain’s ambassador to Saudi Arabia, which has also declared the brotherhood a terrorist organisation.
There is pressure from Gulf states for tougher action, with Qatar facing sanctions from neighbours over its continued support for the brotherhood.
‘Philosophy and activities’
A Downing Street spokeswoman said: “The prime minister has commissioned an internal government review into the philosophy and activities of the Muslim Brotherhood and the government’s policy towards the organisation.”
Initial work has already been carried out by National Security Adviser Sir Kim Darroch, the Times said.
Mass trials of his supporters – which have already resulted in hundreds of death sentences – have met with international condemnation.
The brotherhood – whose political and charitable model has been widely copied – has long had a presence in London, but there have been reports that a significant number of prominent members have fled to the city from Egypt.