For a more realistic model on how schools/childcare are likely to reopen in this country have a look at the timeline set out by Leo Varadkar for Ireland starting next week:
Phase One (18 May)
Outdoor meetings between people from different households will be allowed and childcare for healthcare workers will be opened
Phased return of outdoor workers such as gardeners and repair workers, as well as the opening of retailers which are primarily outdoor
Certain outdoor public amenities will also be opened
Phase Two (8 June)
Household visits will be allowed and plans will be in place to open up business with consideration for safety of staff and customers
Small retail outlets will open with social distancing observed
Open public libraries.
Phase Three (29 June)
Small social gatherings will be permitted and playgrounds will open, while creches, childminders and pre-schools will be available for children of essential workers in a phased manner
Those with low levels of interaction can return to work
Non-essential retail outlets with street level entrance and exit can open.
Phase Four (20 July)
Creches, childminders and pre-schools will be opened for children of all other workers on a gradually-increasing basis.
Those who cannot work from home will return to work
There will be a gradual easing of restrictions for higher-risk services like hairdressers
Opening of museums, galleries and places of worship.
Phase Five (10 August)
Larger social gatherings will be allowed and workers across all sectors can return to the workplace
On a phased basis, commencing at the beginning of the academic year 2020/2021, primary and secondary schools and third level institutions will reopen
At this point there will be further easing of restrictions on high-risk retail services.
Of curse this is all dependent on the level of infection/deaths remaining low.
Even if they did reopen schools in England before the end of summer term, it would be on the basis that not every class would attend school every day, more likely that in Primary it would be one or two year groups each day so that children attend school 2 days out of 5. But for now it is all pure speculation, whatever the newspapers may claim.