Police wearing balaclavas and bulletproof vests and armed with submachine guns smashed their way into the flat, thought to be occupied by two sisters.
Two children and a baby wrapped in a duvet were taken away, witnesses said.
Neighbour Nicola James, 45, said of the family: "When you walked past you would hear them singing Muslim songs. You would hear them chanting through the windows. The gran who used to live there died and since then there has been a lot of comings and goings. I saw the man who was in the video go inside the house. I think he was a boyfriend.
"The woman I think he went out with wore a full niqab. She converted to Islam about 2 years ago."
Another witness said the man was known for handing out radical leaflets.
Police removed a laptop computer and two bags of items from the house.