Up to 30 caravans moved into the field at Oakgrove school on Friday.
It is alleged they “smashed” their way through school gates to enter and refused to budge over the weekend.
During the heatwave a water main in the field has become broken and the traveller children have been cooling off under the result fountain.
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There are also reports of cars driving on the field and churning up the grass, which was due to be used for the school’s sports day on Tuesday.
Police have ordered the encampment to move on today (Monday) but the school has decided to stay closed.
In an email to parents on Saturday, Oakgrove head Ian Tett wrote: “As you may be aware, a large group of travellers have accessed the school site on Friday evening. We have reported this the relevant authorities and we are closely monitoring the situation on the ground.”
He added: “At this stage, I am unsure if we can open on Monday or hold our sports day on Tuesday. I will need to assess the site once they have left the school site and I clearly need to safeguard students and staff.”
There was another email from the school yesterday (Sunday), which stated: “It is with frustration that I must tell you that the secondary site at oaskgrove will not be able to open tomorrow due to unforeseen circumstances.
“The school and Trust has done everything in its legal powers to avoid a school closure, however at the moment the school or site is not safe for students or staff.”
Oakgrove is an ‘all-through’ school catering for more than 2,000 pupils aged from three to 19. The primary school site is open as normal.
Parents have been promised further updates about whether sports day on Tuesday will go ahead on Tuesday. This depends on whether the travellers comply with the order to move on and what state the field will be left in if the do.
One woman said on social media: “My husband just drove by Oakgrove and he says that it looks like there's 100's off them (travellers) and they were driving their cars in circles on their sports field behind the school.
"This is just disgusting. And police cannot do anything about this. They will destroy everything if they stay for a few days longer.”
Another wrote: “They have broken a water main and their kids are playing in the fountain.”
It is understood the encampment was moved on last week from the edge of Northamptonshire.
Some people on social media stuck up for travellers’ rights. But one poster wrote: “I’d be very wary of their behaviour around the pupils and, due to stereotyping and discrimination, the behaviour of the students and their parents towards the travellers.
"You can guarantee at least one of the parents would kick off tomorrow morning. The school could get in serious trouble of a student gets hurt so the best thing all round is to close the school temporarily.”