Opponents claim people in areas of Scotland where the scheme is already running have contacted them and are considering legal action following the judgment.
The No to Named Persons (NO2NP) campaign estimates the legal actions could amount to a multi-million sum after five senior judges ruled that the scheme risked breaching Article 8 of the European Convention on Human Rights.
Education Secretary John Swinney has pledged to press ahead with the scheme despite this week’s legal ruling. He says work will be done to amend the Children and Young People (Scotland) Act 2014.
The Supreme Court found that provision of information sharing in the legislation could result in disproportionate interference with the right to family and private life as defined by Article 8.
The scheme was to be fully rolled out across Scotland next month. But it has already been running in some council areas, where named person schemes have been piloted.
Simon Calvert, of the NO2NP campaign, which took its £300,000 two-year legal battle to the Supreme Court, said: “Many Scottish families whose lives have been already been impacted by illegal intrusions in recent years have approached us and are seeking legal advice.
“There can be little doubt that many more parents are yet to come forward – some unaware that the authorities have been gathering enormous amounts of private information about them, their children and their lifestyles.
“This information has then been transferred and shared between authorities without the knowledge or permission of the families involved.”
Following the court’s decision the Scottish Tories yesterday demanded to know what legal advice the Scottish Government took on its proposal. Shadow Education Secretary Liz Smith said: “The SNP was told consistently that plans to share children’s confidential details were wrong. We now need to know how it was ever allowed to get to this stage.”
Responding to the threat of legal action, a Scottish Government spokeswoman said: “The Supreme Court’s ruling requires changes to be made specifically to the information sharing provisions of the 2014 Act, which have not yet commenced.
“Obviously the judgment does not relate to current practice in relation to information sharing.”