The Digital Economy Bill will lead to sites that do not ask for age verification being blocked.
It received an unopposed third reading from MPs on Monday evening, meaning it is set to become law.
But John Whittingdale, the Tory MP who first tabled the bill in July, is not convinced it will solve the problem.
"One of the main ways in which young people are now exposed to pornography is through social media such as Twitter, and I do not really see that the bill will do anything to stop that happening," Mr Whittingdale said.
