Facebook was urged in June by the Competition and Markets Authority to probe the sale of fake reviews via these groups.
Which? claimed to have uncovered several active groups that recruited people to write fake testimonies.
Facebook said it had removed almost all the groups reported to it and was still investigating the issue.
For its investigation, Which? said it joined 10 separate Facebook groups looking for recruits.
In a 30-day period, it said, recruiters added more than 55,000 posts to the groups that offered free products to people who wrote highly-rated reviews on Amazon.
“It is deeply concerning that [Facebook] continues to leave customers exposed to poor quality or unsafe products boosted by misleading and disingenuous reviews,” said Natalie Hitchins, head of products at Which?
Ms Hitchins said Facebook had to take more action against any group it was told about and be more “proactive” about finding other groups and closing them down.
It said the CMA should consider “enforcement action” to make Facebook act.
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The June call to action by the CMA was also issued to eBay, but Which? said it only found one advert offering five-star reviews for sale on the auction site in its latest probe.
CMA senior director George Lusty said it was “unacceptable” that Facebook groups promoting fake reviews were reappearing.
“Facebook must take effective steps to deal with this problem by quickly removing the material and stop it from resurfacing,” he said. “This is just the start – we’ll be doing more to tackle fake and misleading online reviews.”
A spokesman for Facebook said: “We don’t allow people to use Facebook to facilitate or encourage false reviews.”
It said it had removed nine of the 10 groups Which? reported to it and was investigating the remaining one, it said.
The social network added that it was improving the tools and technologies it used to find the groups.