“It’s going to be five years before anybody puts his head above the parapet again.” That’s how Michael Weatherly, a member of the British Parliament and intellectual property adviser to Prime Minister David Cameron handicapped the prospects for a fresh legislative push against online piracy in the United States.

Following the defeat in 2012 of the Stop Online Piracy Act, movie companies and other advocates for copyright owners both here and in Britain have been pointed toward voluntarism. That has meant, among other things, agreements under which Internet service providers send escalating warnings to those who are believed to be downloading copyrighted material illegally.

But at a news briefing in Los Angeles on Wednesday, Mr. Weatherly, a plainspoken type, also talked of escalating pressure — legal and otherwise — on those who advertise on sites where illegal downloading is taking place. “There are some laws in place, but we might need to beef up a couple of them a bit more,” suggested Mr. Weatherly, who spoke of an effort to “strangle the advertising revenue from the illegal sites.”

Mr. Weatherly was in Los Angeles to meet with entertainment executives, with a particular eye toward cloning an American version of his favorite anti-piracy enterprise. That is a government-sponsored competition, called “Rock the House,” which gives prizes to young musicians, while drilling them with a message: You’ll never have a career in entertainment if your audience keeps stealing the goods.