Hamid Patel, chief executive of the Star Academy group, is calling for an urgent recognition that schools will not have capacity for a full return.
He says schools need a decision on social distancing to be able to start making plans.
The government has said it wants all schools and pupils back for the autumn.
Mr Patel, who is also on the board of the education watchdog Ofsted, says that with 2m distancing in place, no more than 50% of secondary pupils could attend, and in some schools it would be lower.
Primary pupils are being kept in “protective bubbles” of no more than 15 pupils and for secondary schools going back in September, the guidance calls for a distancing of 2m.
The lack of space in primary schools, because of small groups needing more classrooms, has already stopped primary schools bringing back all year groups.
If the ambition is “genuinely for all schools to reopen in September, open and honest discussions are needed” about what “workable solutions” could be achieved, says Mr Patel.