The CCG represents all GP services and referrals in the area.
They will now have until August 31 to opt out of sharing their personal information.
The programme, GP Data for Planning and Research, would put the medical histories of 61 million patients across England into a new database.
NHS Digital figures show the number of patients registered with GPs in England increased over the last year, from 60.4 million in June 2020 to 60.9 million this month.
In NHS Cambridgeshire and Peterborough CCG, the number of patients rose by 9,536.
The launch was delayed to September 1 following complaints from privacy campaigners and doctors that people did not have enough time to understand what was happening and to act if they objected to their data being released for things such as research.
Simon Bolton, chief executive of NHS Digital, said: “We take our responsibility to safeguard the data we hold incredibly seriously.
“We intend to use the next two months to speak with patients, doctors, health charities and others to strengthen the plan even further.”
The scheme will collect information on people’s treatments, referrals and appointments over the past 10 years, alongside other data from medical records held on GPs’ systems.
Information will be accessed by organisations “which will legitimately use the data for healthcare planning and research purposes”, and all requests will be subject to independent oversight and scrutiny, NHS Digital said.
It added that patients can opt out of sharing their data at any time, though it will not be applied retrospectively.
Anyone wishing to opt out of GPDPR entirely should therefore do so before September 1.
The data will be pseudonymised to ensure patients cannot be directly identified.
But campaigners say pseudonymous is different from anonymous, meaning peoples’ identities will be disguised but could later be re-identified.
Cori Crider, director of digital privacy group Foxglove, said: “The Government must make sure every single patient in England is meaningfully informed about what is happening to their data.
“How will the Government guarantee that for people who aren’t online, like the 67 per cent percent of older people not digitally connected?
“This data belongs to patients, and they fund the NHS, so it should be their choice.”
The Royal College of GPs also welcomed the delay, but said safeguards must be in place to ensure data is not used inappropriately.
Professor Martin Marshall, chairman of the Royal College of GPs, said: “It is essential that this time is used to properly communicate with the public and with clinicians so that patients and GPs have trust in the programme.
“Surveys show that most patients are happy for their data to be used for legitimate planning and research purposes, but this must be built around trust.”