The complaint has heightened already fraught tensions between the two organisations, and has led Privacy International to seek legal advice after Google suggested that the group is "far from impartial".
Street View, launched in the UK last week, gives a 360-degree view of particular streets by merging photos collected by Google drivers using car-mounted cameras.
Google was given authorisation to launch the system in the UK because it promised to use blurring technology to hide people's faces. Citizens who are still able to distinguish themselves can ask for the image to be removed entirely.
Immediately after the mapping system went live, Google had to pull images that upset early testers who had identified themselves in the photos. For example, Google took down a man seen vomiting in Shoreditch, and another man outside a Soho sex shop.
Privacy International has argued that the face blurring technology is not working effectively. It has also claimed that pulling images after users feel that their privacy has been violated is not an adequate safeguard to protect people's liberties.
"Why, under this reasoning, should not all commercial organisations be permitted to collect limitless volumes of personal data without consent on the promise that specific items of data will be removed on request?" asked Simon Davis, Privacy International director, in a letter to UK Information Commissioner Richard Thomas. "Is this the new legal guidance for supermarkets, banks and hotels?"
A spokesperson for the ICO said in response: "Individuals who have raised concerns with Google about their image being included - and who do not think they have received a satisfactory response - can complain to the ICO."
But Privacy International, which has registered concerns regarding Street View since May 2008, wants the ICO to take "immediate action" to prevent what it believes is a violation of the Data Protection Act.
Davis has demanded that the ICO consider how the technology has caused a " substantial threat" to some individuals, and that "the extent of intrusion into the homes of some complainants is unlawful".
One example he gave was of a woman who has been moving house for years to escape a violent former partner and the distress she felt when she identified herself outside her house on Street View.
Google's response to the complaint has been to reiterate the popularity of the tool, and that images that cause distress can be taken down.
"Of course, if anyone has concerns about the product or its images they can contact us and we look forward to hearing from them," a Google spokeswoman added.
Google has also hit out at Privacy International, declaring that the letter was an "entirely predictable publicity stunt by an organisation that is far from impartial when it comes to the issue of Google and privacy".
Relations between the two have been difficult in the past couple of years. Privacy International's first privacy ranking published in June 2007 gave Google the lowest ranking among the major companies it surveyed.
Google's response to the scoring, and to many subsequent privacy complaints made by Privacy International, has been to point to "a conflict of interest" arising from Microsoft's Casper Bowden being an advisory board member.
Davis said that he plans to seek legal advice after Google's latest accusation that the organisation is biased. "In no circumstances do we allow the impartiality of the organisation to be influenced," he said. "We will not stand by while our organisation is shot down."
New Vikendi map adds snow, snowmobiles and new aural and visual twists
Faults and bad weather ground SpaceX, Blue Origin, Arianespace and United Alliance
New regulation expected to cut greenhouse gas emissions by about 17 million metric tonnes between 2020 and 2050
Molybdenum ditelluride is a two-dimensional material that can be easily stacked into multiple layers to create a memory cell