Prince William has said criticism about his privileged lifestyle and many residences drives him to try to end homelessness in Britain.

The heir to the throne was challenged to respond to jibes about his three homes and 135,000-acre Duchy of Cornwall estate for a two-part ITV documentary airing this week.

In Prince William: We Can End Homelessness, viewers hear a recording of LBC radio host James O’Brien citing criticism from Graham Smith, the chief executive of Republic, the anti-monarchist group, who says homelessness is about government policy and investment, and won’t be stopped by charity or royal patronage.

Asked how he feels about the criticism of Homewards, his five-year programme designed to show others how homelessness can be ended, William says: “I think if I answered every critic, I’d be here all day. But you know, criticism drives you forward.”

He adds: “I think it’s right to question but I think, ultimately, we are pushing forward to deliver change and hope and optimism into a world that frankly has had very little of it for a long time. I hope I can bring something that’s not been done before.”

The documentary, which airs on Wednesday and Thursday, follows him through the first year after launching Homewards. William is seen touring Nansledan, near Newquay, where the duchy is building 24 homes.

“I’m not sitting here saying I’m going to solve the entire world’s homelessness problems. But I am going to show people how to prevent homelessness,” he says.

More than 350,000 people in Britain lack a permanent home. The number of homeless people, or at risk, aged between 16 and 24 is estimated to have risen to more than 130,000.

The prince tells the documentary team he has discussed homelessness with his three children, George, Charlotte, and Louis on the school run. In Windsor, where they live, the local council was dealing earlier this year with 101 homelessness cases and there were 25 rough sleepers.

“The first few times I thought, do I bring this up? Or should I wait and see if any of them noticed? And sure enough, they did, and they were just sort of in silence after I had said what was going on,” he tells the film-makers. “And I do think it’s really important that you start those conversations when the children are small, so that they understand the world around them and they’re not just living, you know, in their own little worlds.”