NHS England has admitted the campaign to educate patients about care.data has been inadequate.
Last month, all households in England were send leaflets about the scheme, which outlines the benefits of sharing medical records and information about treatment outcomes.
Yet the system also allows drug and insurance companies to buy pseudonymised data about patients.
The information commissioner's office has criticised the campaign for failing to explain what data is involved and how patients can opt out.
Dawn Monaghan from the commissioner's office said it is "not clear enough" in the leaflets or on the website, what data will be used.
Speaking on the BBC Radio 4 Today programme, she said: "What it says is that you can object to your personal confidential information leaving the GP surgery. We are not sure that without further explanation… whether people will understand what that means."
Tim Kelsey, the NHS national director for patients and information somewhat agreed. He told Today that perhaps NHS England "haven't been clear enough about the opt-out".
He said: "Let me be absolutely clear now. People who don't trust the NHS to manage their data securely now have a new right to opt out of this scheme. To be honest, all they need to do is contact their GP to opt out. We are doing this because it is vital that we help the NHS care better for the patients it is serving."
The public will not know who has their medical records, or how their data will be used, privacy campaigners have warned.
Phil Booth from medConfidential said patients' medical records would be identifiable unless they opted out.
He said: "The main concern is this whole new class of data that care.data opens up, which is individual level, pseudonymised data, that is data which is not anonymous but which contains individual patient's medical information and which can be re-identified. The biggest risk here is undermining people's trust."
However, Kelsey said that patients can not be re-identified using pseudonymised data.
"Doctors and nurses on the front line need to understand whether their service is as good as it could be. To do that they need individual level data. It is not identifiable … This data is stripped of all the identifiers."
He added: "We operate the NHS on only a slim sliver of hospital data. And in 25 years there has never been a single episode in which the very strict rules have ever compromised a patient's confidentiality."