LONDON -- On a Friday night in East London, activists with a group called "Britain First" took to the streets for what they call a Christian patrol. Our cameras went along with them as they entered a "predominantly Muslim occupied area," according to one of the group's members.

It wasn't long before there was a confrontation.

"What are you filming me for?" shouted a passerby.

"This ain't your area pal, it's a Christian area, always has been," shouted back Paul Golding, the 32-year-old leader of Britain First.

Britain First leader Paul Golding at a rally Britain First

A former truck driver, Golding has been convicted for harassment. While it's difficult to know how many supporters he has, the group's Facebook page has more than half a million likes.

"We've got to stop putting our heads in the sand and allowing this Islamic extremist cancer to grow in our country," Golding told me. "We've got to confront it head on and that's what we seek to do."

"Do you believe that a confrontation is inevitable?" I asked.

"When they're 40 percent or 50 percent of the population and they've got a huge block in parliament, I imagine there will be a civil war in this country," Golding answered.

Golding says the Christian patrols are a response to Muslim patrols, in which Islamic extremists have harassed people on the streets for behavior that they deem to be un-Islamic.

We accompanied a young radical - Abu Rumaysah - on a patrol last October on assignment for "60 Minutes."

"Ultimately, I want to see every single woman in this country covered from head to toe," Rumaysah told me. "I want to the see the hand of the thief cut. I want to see adulterers stoned to death. I want to see Sharia law in Europe and I want to see it in America as well."

Abu Rumaysah walks with CBS News' Clarissa Ward CBS News

Golding says no one should be allowed to claim that any neighborhood is Muslim.

"That's bang out of order and he shouldn't be doing that, he's a foreigner, he's a guest in our country," said Golding.

"They're not guests, they're British citizens," I countered. "This is their home."

"If your loyalty is to Islam then in our opinion, you're not British anymore."

The majority of British people would disagree. But the fear is that with the threat of more terrorist attacks, Britain First's popularity will continue to grow.