Heads say they are mounting military-style operations to bring teenagers back to school in England in smaller groups from Monday next week.
The ASCL heads union estimates 90% of secondaries will be welcoming some pupils with exams next year into class.
The government wants schools to give Year 10 and 12 pupils some face-to-face time with teachers before term ends.
But safety guidelines to minimise virus spread mean only a quarter of these year groups can be on site at a time.
This is will not be a return to full-time schooling, more a range of review sessions and extra support, with priorities given to pupils who have struggled with remote learning.
The union’s estimate is based on a responses to a survey by ASCL from around a quarter of the 3,229 secondary heads, college principals academy chief executives in England.
It is the first indication of what is likely to happen from Monday next week.
It suggests where wider opening is not happening it is due to local concerns about the rate at which the virus is spreading. In these cases, wider opening may start a week later, the snapshot survey suggests.
Geoff Barton, ASCL’s general secretary, said: “Schools and colleges have moved mountains to support children through the coronavirus pandemic with emergency provision, remote learning, and now bringing in more children, in extremely challenging circumstances.
“This is akin to something between a military operation and an exercise in mathematics.
“There are many practical safety measures to put in place, as well as allocating small groups of eligible pupils to available teachers, while ensuring no more than a quarter of the cohort is on site at any time.
“School and college staff deserve great credit for all they have done over the past few months, and all they are doing now.”
It comes days after the Education Secretary Gavin Williamson said he was abandoning plans to require schools to bring all pupils back for a month before the summer break.
With secondary schools only otherwise open to key workers and vulnerable children, the vast majority of pupils will remain out of school until September at least.
Mr Barton stressed that it was important now that the government “works with the profession, as a matter of urgency, on a national plan for the recovery of education”.
There needed to be a “particular focus on what happens from September, and how we support the learning and wellbeing of all children disrupted by this crisis”, he added.
He echoed earlier calls by other teaching unions, politicians and academy chain bosses, that a plan is developed as soon as possible in order to give schools and colleges time to prepare for their “vital mission”.
Nearly two-thirds expect to bring in all eligible pupils other than those who are shielding and self-isolating.
And a quarter said they would only be bringing in some pupils, due mainly to concerns of parents or transport arrangements.
The government insists it has been working with the teaching profession and partner organisations to do its best for children and this week said it was working on an extended summer catch-up plan for pupils.
Local councils are calling for more details on the plans.
Chairman of the Local Government Association’s children and young people’s board, Councillor Judith Blake, praised the efforts made by teachers and school staff.
She added: “With the summer holidays rapidly approaching, we are calling on the government to urgently start a conversation with local authorities and schools to provide clarity on what exactly it is proposing to help children catch up on any schoolwork they may have missed out on during lockdown.”
Meanwhile, the Welsh government has published new guidance on the measures schools should consider when reopening, including outside learning, teaching in small groups, and pupils eating at their desks.
Schools in Wales will reopen to all age groups from 29 June, but only a third of pupils will be in classes at any one time.
First Minister Nicola Sturgeon says Scottish schools will reopen from 11 August, but with some continued home learning.
In Northern Ireland, ministers have set a target date for some pupils to go back on 17 August, with a phased return for the rest in September.