And even the leader of the council has revealed he is "very worried" this week's easing of lockdown restrictions could lead to a rise in the city's currently low infection rate.
If this happens, the council will step in and compulsorily close schools, he has warned,
Most local schools have remained open throughout the coronavirus restrictions for the children of key workers and vulnerable children - but from today pupils in Reception, Years 1 and 6 were able to return.
MK has 89 primary schools, and 60 of them fall under the jurisdiction of the council.
Of these, 25 opened today while a further 13 had training sessions and plan to open on Wednesday.
Another 22 schools are phasing their reopening over the next few weeks. But four council schools in MK will not open at all during lockdown because they do not have the space for social distancing.
While some of the school plan to reopen with normal hours, a significant number will close for the day or half day on Fridays to allow for deep cleaning.
Milton Keynes Council has vowed to support any decision local schools take, including a wish to stay closed. And the council will also support parents who currently do not feel able to send their eligible children to school.
Pete said: "MK Council will always put the safety of staff and pupils first. In Mk we currently have a low infection rate and low R rate."
But he admitted the wider risk was that, since the reopening of schools was announced, the government has made a "raft of other changes" and announced lockdown restrictions will be eased from today or the near future.
"Our current position is that with a low R rate, schools are best placed to make the choice locally and respond to staff and parent concerns. However, we are not in a position to be complacent and I am very worried there are too many changes, too soon," he said.
Pete added: "If our infection rate rises, we will act and not be afraid to recommend closing schools or any other businesses to control any increase as necessary."
A spokesman for MK Council said: “We’ve been working closely with school leaders on their individual re-opening plans. Many schools in Milton Keynes have pre-planned inset days today and tomorrow. We expect 90% of our primary schools will be open to eligible children by 05 June.
“We expect all schools in Milton Keynes to follow DfE guidance around re-opening for eligible year groups. Experienced school leaders will decide how best to achieve this for individual schools and will communicate their plans with parents. We will continue to work closely with schools to guide and support them through this challenging time.”