Anjum Anwar was speaking after the documentary, called "What British Muslims Really Think", surveyed 1000 British Muslims and explored their beliefs about various social issues including national identity, violence, sexuality and gender relations.
She was formerly the Dialogue Development Officer at Blackburn Cathedral, and appeared in the documentary herself.
Some have criticised 'What British Muslims Really Think', citing previous polls which have showed them in a significantly more positive light.
Some of the things "What British Muslims Really Think" found:
- 91% of British Muslims feel a strong sense of belonging to their local area, higher than the national average of 76%;
- 86% of British Muslims feel a strong sense of belonging to Britain (86%), higher than the national average of 83%;
- 78% would like to integrate into British life on most things apart from Islamic schooling and some laws;
- 52% do not believe that homosexuality should be legal in Britain;
- 34% would inform the police if they thought somebody they knew was getting involved with people who support terrorism in Syria;
- 32% refuse to condemn those who take part in violence against those who mock the Prophet.
Speaking after the documentary Baroness Sayeeda Warsi, the peer and former chairman of the Conservative Party, said British Muslims had made more progress in changing their attitudes on various social issues since they arrived in Britain in the 1950s than the Church of England and the Conservative Party had over the same period.
Baroness Warsi (below) also said it was hypocritical for people to specifically criticise conservative Muslims for their views - for example regarding homosexuality or gender relations - when many conservative Christians and Jews also believe the same or similar things.
She said: "There is social conservatism, maybe even social intolerance, but most religious communities on the issue of homosexuality have been on a journey on this.
"So has my own party, so has the Church of England.
"But our community in Britain is 50 or 60 years old - we have moved faster than my party, which has been around much longer, or the Church."
Anjum Anwar told Premier's News Hour: "1081 people were interviewed, and three million were demonised last night.
"The fact is that you always have a certain amount of people in those communities who have those views.
"One can play with statistics. The point is if somebody is thinking of committing a criminal act he should be arrested - but we do not demonise the whole community.
"The documentary was supposed to be based around community cohesion - I didn't see much cohesion.
"Mr Trevor Phillips has not been able to differentiate between assimilation and integration. I think the documentary was flawed"
Listen to Premier's Alex Williams speaking to Anjum Anwar on the News Hour:
