The decision comes at a time when online privacy and the “right to be forgotten” is being increasingly debated by politicians.
The Scottish activist, who has asked not to be named, is prominently featured on Redwatch, an online platform which shares pictures, contact details and employment history of alleged “Marxists” – usually anti-fascist campaigners, trade unionists and journalists.
The website has previously been described as a “practical instrument for criminal activity, violent assault and political intimidation” by Labour MP Angela Eagle.
Redwatch invites readers to send in details of “your local red scumbags”, adding that “we want their names, addresses, phone numbers, photographs, work details – anything and everything about them to publish here”.
The campaigner e-mailed Google directly last month after discovering a link to Redwatch was among the top search results for their name.
In an e-mail seen by The Scotsman, they asked for the search result to be delisted, in line with EU law.
The activist said: “I was surprised to learn that Google considers access to outdated details about me on a site run by neo-Nazis to be ‘justified by the public interest’.
“If featuring on Redwatch – a site which operates on a manifesto of making ‘traitors... pay for their crimes’ – doesn’t qualify as harassment, it’s hard to see what does.”
Several photographs and personal details of the activist have been on the site since at least 2013.
“In 2009 I was involved with organising demonstrations against what, at the time, seemed like a growing threat from the far-right,” they said.
“The BNP were active in Glasgow and trying to build on their success in the European elections that year, and the Scottish Defence League had just announced their first demonstration.
“Soon enough, the faces of myself and other young people at those protests appeared on Redwatch, alongside names and other details.
“Although they were photos that had been harvested from other websites, it was clearly intended to be threatening. The whole purpose of the website is to harass anti-fascists and it has been linked to violent attacks and death threats south of the Border.”
A spokeswoman for Google said: “Our search results are a reflection of the content across the web. These results don’t reflect Google’s own opinions or beliefs – as a company, we strongly value a diversity of perspectives, ideas and cultures.”
Google added it “strived to give users a breadth of diverse content from variety of sources” and was committed to the principle of a free and open web.
The California-based tech giant only removes pages from search results under very narrow circumstances, such as when a page or a site violates its own webmaster guidelines, if it believes it is required to do so by law, or at the request of the webmaster who is responsible for the page.
A European Court of Justice ruling in May 2014 required search engines in Europe to remove links to information relating to ordinary individuals who complain that it is outdated or irrelevant.
Google said in the month following the ruling it received more than 70,000 requests relating to a quarter of a million websites.