Speaking to the BBC on Wednesday, Buckland said: "I'm not going to sit here and pretend suddenly on the first of June everything will be uniform," admitting the track and trace system which includes a mobile phone app "won’t necessarily be as widespread and as full-blown as we would like."
When he originally announced plans to reopen schools, Education Minister Gavin Williamson said track and trace would "create an inherently safer system" for pupils and staff returning to their classrooms.
The British National Education Union (NEU) has called the proposed reopening plans "reckless," and urged the government to share the data and models they are basing their evaluations on.
"We are asking and advising leaders not to start planning for 1 June as we do not think it is safe to do that at this stage," a statement from NEU on Tuesday said, adding they are in "urgent talks" with the Department for Education.
In an op-ed for the Daily Telegraph newspaper, the chairman of the BMA's Public Health Medicine Committee Dr. Peter English wrote on Tuesday: "We know that the longer children are kept away from the classroom, the greater the harm to their education, life opportunities and wellbeing. For disadvantaged children, this harm is even greater. A focus on arbitrary dates for schools to reopen is polarising."
"The BMA wants schools to reopen as soon as it is safe to do so and the evidence allows – this could be before June 1 or after. But a zero-risk approach is not possible. This is about 'safe' being an acceptable level of risk," he added.
About 85% of British teachers said they do not think it will be safe to return to school on June 1, according to a survey published by the National Association of Schoolmasters Union of Women Teachers (NASUWT) on Tuesday.