The Fundraising Regulator named the charities for failing to log on to the FPS to collect requests by members of the public to stop contacting them by email, telephone, post or text. It also referred them to the ICO.
The two regulators warned the charities, which are supposed to act within 28 days of suppression requests being made, that they could be in breach of data-protection regulations.
But an ICO spokeswoman said yesterday that it was not taking any further action.
"The ICO has written to these charities, reminding them that they must act lawfully and responsibly in protecting people’s personal data and in how they communicate with them," she said.
Asked why it had decided not to pursue matters, she added: "The evidence does not meet the threshold for enforcement action, so we are engaging with the charities and encouraging them to comply with the law.
"However, they have been warned that, if they fail to act on people’s rights under data-protection legislation, the ICO reserves the right to take formal enforcement action."
This month's list, which was revealed on Monday, contains 49 charities.
Fourteen that were named last month – including the Challenge Network – have been removed.
About 8,300 people have submitted more than 25,000 suppression requests since the launch of the FPS in 2017.