Subscribe to your cable or satellite provider's option that includes BBC America. Many popular British comedies, dramas and reality TV shows air on this American channel, along with British news programs and movies.
Get a subscription to Netflix or Hulu. Both services are increasing the amount of British programming they have available to viewers. Their options are not limited by location, so viewers in the U.S. have access to the same shows as viewers in Britain do.
Pay attention to your local public broadcasting station's schedule and check for British shows. PBS often airs them, such as the "Masterpiece" series, and watching them does not require any kind of subscription.