According to a joint letter seen by the Daily Telegraph, the councils said there was a "significant amount of vaccine" to go around.
The paper reports nursery workers have been offered jabs, and the two authorities secured vaccinations for children’s services staff in secondary schools.
But the two Conservative-controlled authorities said, in a joint statement on Wednesday, that they have since "clarified to schools and early years settings… that at this stage, the eligibility for the vaccine will only include staff who provide personal care and support".
A teaching assistant from the county took to Twitter to say: "So all education staff in Cambridgeshire and Peterborough were told we could get a vaccine on Monday and on Tuesday were told that it was a mistake and were not getting it anymore."
The priority list has been decided by the Joint Committee on Vaccination and Immunisation (JCVI) – an independent expert advisory committee.
The top four priority groups are now eligible to get their coronavirus vaccine in England, meaning people who work in health and social care, as well as everyone over the age of 70, care home residents and those who are clinically extremely vulnerable can now be contacted for an appointment.
The top priority groups are the over-80s, care home residents, and NHS and social care staff, and the Government said it will remain the priority to vaccinate them.
But there have been reports that some people outside of these priority groups have been offered vaccines.
In the joint statement, Peterborough City Council and Cambridgeshire County Council said: "Our top priority is to ensure the vaccine is offered to those who are most vulnerable.
"In line with JCVI national priorities, this includes residents of care homes, the over-80s and those providing frontline health and social care.
"By offering to these groups, we are following the national guidelines and Cambridgeshire County Council, Peterborough City Council and the local NHS are working hard to ensure these groups receive their jabs and not a drop of vaccine is wasted.
"As part of this work, other groups on the national priority list levels three and four are beginning to be invited to come forward for vaccinations.
"Today (Wednesday), we have clarified to schools and early years settings across Cambridgeshire and Peterborough that at this stage, the eligibility for the vaccine will only include staff who provide personal care and support.
"But we have also started to collect data from schools and other priority groups to be ready should the national guidelines allow us to provide wider vaccination at a later stage to people in these settings.
"We will continue to prioritise people for vaccines following JCVI guidelines."
On Monday, vaccines minister Nadhim Zahawi suggested he would be in favour of including retail workers in a priority grouping with teachers and police.
Speaking to ITV’s Good Morning Britain, he said: "When we enter phase two, we will work with the JCVI to look at the priority.
"My instinct is that anyone who, through no fault of their own, has to come into contact with the virus in much greater volume and probability should be protected – teachers, policemen and women, shop workers, all those who need that additional protection.
"Now, some of them will be captured in the top nine categories anyway if they are clinically vulnerable, for example, or in that age group of the over-50s which are in category nine, effectively.
"But phase two – of course we’ll be guided by the JCVI – but my instinct is that if you work in a job, a shop worker, policemen or women, any other profession which brings you into contact with the virus unfairly, then I think you should be prioritised."
A government petition requesting that priority be given to teachers, school and childcare staff for Covid-19 vaccination has gained 545 signatures from the Peterborough constituency, and 1,220 in North West Cambridgeshire. In total, more than 480,000 people in the UK have signed.