The Archbishop made the comments in his new book to be released next week, called On Rock or Sand.
He also said politicians are selling a "lie" to the public when they say economic growth will fix Britain's social problems, and that a culture of "rampant consumerism and individualism" has "dominated" the UK since the era of Conservative Prime Minister Margaret Thatcher.
In a YouTube video introducing his book, Most Revd Sentamu said: "One of the greatest challenges that faces our nation has to do with income inequality. That's the biggest giant we have got to slay. Income inequality traps a lot of people... on poverty wages."
Speaking to the Daily Telegraph, David Cameron said: "I haven't seen this report in all its detail so I will study it, but from an early reading of The Daily Telegraph I profoundly disagree with some of the things that they are saying.
"Far from leaving cities behind, we're rebalancing the economy and you can see real growth in cities like Birmingham and Manchester and Leeds - indeed some two-thirds over the last year has come from outside London and the South East.
"And some of the places where jobs are growing fastest and apprenticeships are growing fastest, where exports are growing fastest are not in London or the South East.
"Also, we are tackling poverty by giving 1.75million more people a job in our country. Actually under this Government inequality has fallen so I don't think the picture they paint is accurate.
"I speak pretty vigorously in defence of the excellent economic and social record of this government.
"The fact is you can't do any of these things in terms of tackling poverty, growing opportunity, rebalancing the economy unless you have a strong economy and we have restored or are restoring the strength of the British economy."
