Nigel Farage has backed the "basic principle" of Enoch Powell's warning that mass immigration can make people feel like strangers in their own country from the Tory politician's 1968 "rivers of blood" speech.

The Ukip leader was read several lines of the infamous speech on Sky's Murnaghan show and agreed that it was true for "a lot of England" – without being told who had spoken the words.

The extract was about the impact of immigration, saying "the indigenous population found themselves made strangers in their own country, their wives unable to obtain hospital beds in childbirth, their children unable to obtain school places, their homes and neighbourhoods changed beyond recognition".

Told the origin of the quote, Farage said the central principle was right, as Powell was warning about tension that can happen when you have a large influx of people into an area.

Asked if Powell "saw it coming", the Ukip leader replied: "Well no … for different reasons, for different reasons and on a completely different scale.

"I mean when immigration was being discussed in the 60s and 70s and 80s we were talking about an annual net inflow to the country of between 30,000 and 50,000 people.

"What we have had in the last 13 years is net 4 million extra migrants who have come to Britain so we are dealing with something now on a scale that hitherto we couldn't even have conceived."

Farage attacked David Cameron for not doing enough to limit immigration, arguing that only people earning the national average wage should be allowed into Britain and that they should have to wait five years before claiming jobless benefits.

He also mocked the prime minister on Twitter for his focus on the issue: "David Cameron seems to be trying to sound like me. But the thing is, I believe in what I say."

In 2008, Farage controversially named Powell as his political hero in an interview with Total Politics magazine, although he said he was not thinking of the "rivers of blood" speech that got the Tory politician sacked from Ted Heath's shadow frontbench team.

"I would never say that Powell was racist in any way at all. Had we listened to him, we would have much better race relations now than we have got," he said at the time.