An open letter is calling on the County Council to reject plans to reopen primary schools on Monday.
250 parents, teachers and residents have now signed the letter, started by the Oxford Trade Union Covid Action group.
It calls on Oxfordshire County Council not to open schools until it's safe, saying parents and staff are 'very concerned.'
The group is also hosting an online public meeting today, supported by the Oxfordshire NEU, to 'help organise teachers and parents unhappy with the governent's plans.'
The prime minister wants reception, year one and year six pupils to resume lessons from 1 June, as the coronavirus lockdown eases.
More than two-dozen councils in England have said they will support schools that decide not to reopen on that date.
Here, Oxfordshire County Council said last week that it the safety of pupils, teachers and residents is its 'absolute priority', but the Government will decide when schools might re-open.
It also said it was in regular contact with the Department for Education, adding that the government had published several sets of guidance for schools.
Ian Mckendrick, a nurse from Oxford Trade Union Covid Action group said, "It is the lockdown alone that is bringing the rate of infection down.
"There is no other tested strategy in place, and a real risk infection rates will rise, flooding the NHS with new cases if the lockdown is eased too soon."
Leigh Seedhouse, Joint District and Branch Secretary for Oxfordshire NEU said June 1st was 'simply too early to go back.'
He said: "By going ahead with this dangerous decision, the government is further risking the health of our communities and the likelihood of a second spike."
Leigh also added that as well as track and trace an, 'we need to see regular testing and PPE for those who need it.'
The Oxford Trade Union Covid Action group is also supporting two national days of action against an unsafe return to schools tomorrow (28/05) and Monday.