The Patriot News Agency website popped up in July, soon after it became clear that Donald J. Trump would win the Republican presidential nomination, bearing a logo of a red, white and blue eagle and the motto “Built by patriots, for patriots.” Tucked away on a corner of the site, next to links for Twitter and YouTube, is a link to another social media platform that most Americans have never heard of: VKontakte, the Russian equivalent of Facebook. It is a clue that Patriot News, like many sites that appeared out of nowhere and pumped out pro-Trump hoaxes tying his opponent Hillary Clinton to Satanism, pedophilia and other conspiracies, is actually run by foreigners based overseas. But while most of those others seem be the work of young, apolitical opportunists cashing in on a conservative appetite for viral nonsense, operators of Patriot News had an explicitly partisan motivation: getting Mr. Trump elected. Patriot News — whose postings were viewed and shared tens of thousands of times in the United States — is among a constellation of websites run out of the United Kingdom that are linked to James Dowson, a far-right political activist who advocated Britain’s exit from the European Union and is a fan of President Vladimir V. Putin of Russia. A vocal proponent of Christian nationalist, anti-immigrant movements in Europe, Mr. Dowson, 52, has spoken at a conference of far-right leaders in Russia and makes no secret of his hope that Mr. Trump will usher in an era of rapprochement with Mr. Putin.