The UK’s Times and Sunday Times are putting up search walls in addition to pay walls.

The papers, which plan to start charging users for access to their newly redesigned Web sites in late June, will prevent Google and other search engines from linking to their stories.

Although they are not the first papers to erect pay barriers around their content, the papers are going a step further by making most of their site invisible to Google’s Web crawler. Except for their homepages, no stories will show up on Google.

The papers are betting that loyal readers will covet access to scarce content. Critics say the move will make it tougher to attract new readers who discover content by searching the Web.

The papers launched new, separate sites yesterday. Both papers, which, like The Post, are owned by News Corp., will make the sites free for registered customers until late June.

News Corp. chief Rupert Murdoch has taken aim at Google in the past for profiting from publishers’ content on the Web without paying for it. The British papers are the first within the News Corp. fold to jump off the search bandwagon.

The Times’ move will be closely watched in publishing circles. The Wall Street Journal, also part of News Corp., and The Financial Times charge readers for access but let Google link to their stories.

The New York Times is going back to a pay model in 2011 after ending TimesSelect, a service which charged for access to some content such as columns, in 2007.