In her first major test of being tough on extremism, Theresa May, the new Home Secretary, said she was banning Zakir Naik from entering the UK.

Dr Naik, a 44-year-old Indian televangelist, had been due to give a series of lectures at arenas in Wembley Arena and Sheffield.

The Home Secretary can exclude or deport an individual if she thinks that their presence in the UK is not conducive to the public good.

There had been speculation that Dr Zaik would be allowed into the UK. However Mrs May said she was excluding him because of the “numerous comments” he made were evidence of his “unacceptable behaviour”.

This behaviour applies to anyone who writes or publishes material which can “foment justify or glorify terrorist violence” or “seek to provoke others to terrorist acts”.

Mrs May told The Daily Telegraph: “I have excluded Dr Naik from the UK. Numerous comments made by Dr Naik are evidence to me of his unacceptable behaviour.

“Coming to the UK is a privilege not a right and I am not wiling to allow those who might not be conducive to the public good to enter the UK.

“Exclusion powers are very serious and no decision is taken lightly or as a method of stopping open debate on issues.”

Home Office sources said Dr Naik had been filmed on a website making inflammatory comments such as “every Muslim should be a terrorist”.

He said: “When a robber sees a policeman he’s terrified. So for a robber, a policeman is a terrorist. So in this context, every Muslim should be a terrorist to the robber.”

He has also been filmed saying: “There are many Jews who are good to Muslims, but as a whole … The Koran tells us, as a whole, they will be our staunchest enemy.”

In a web posting from 2006 he said: “Beware of Muslims saying Osama Bin Laden is right or wrong. I reject them … we don’t know.

“But if you ask my view, if given the truth, if he is fighting the enemies of Islam, I am for him. I don’t know what he’s doing. I’m not in touch with him. I don’t know him personally. I read the newspaper.

“If he is terrorising the terrorists, if he is terrorising America the terrorist, the biggest terrorist, every Muslim should be a terrorist.”

He is also reported to have said suggested that western women make themselves “more susceptible to rape” by wearing revealing clothing.

He reportedly said: “Western society has actually degraded [women] to the status of concubines, mistresses and social butterflies, who are mere tools in the hands of pleasure seekers and sex marketeers”

Last night Patrick Mercer MP, the former chairman of the Commons counter-terrorism committee, said: “This is really good news. It shows that firm Government action can be taken against people.

“This is exactly the sort of man who we want to exclude from this country.”

Dr Naik has been named as the third most popular spiritual guru in India and was judged in 2009 to be 82nd in a list of India’s most powerful people.