The university said all were now isolating, as were those they have come into contact with. Seventy-eight of the 770 who tested positive are symptomatic, a spokesperson said.
Northumbria University is among more than 50 institutions to have confirmed coronavirus cases in recent weeks after thousands of students returned to campuses.
Glasgow University has had 172 confirmed cases while the University of Manchester recorded 221.
A spokesperson for Northumbria University said: “The increase in numbers comes in the week after students returned to university and reflects the good access to and availability of testing, as well as rigorous and robust reporting systems.
“In parts of the UK where universities started term earlier, numbers of student cases surged in induction week, and then reduced.
“We are making it clear to students that if they break the rules they will be subject to fines from police and disciplinary action by the universities which may include fines, final warnings or expulsion.”
However, lecturers have since claimed they were encouraged to take on a greater than average amount of face to face sessions despite concerns from staff.
One employee, who asked to be made anonymous, said: "We have high anxiety levels among staff and students who have a sense that the establishment is not listening to those anxieties about face-to-face teaching.
"There's a lot of frustration because almost everything that we deliver face-to-face could be done much more safely online.
"There's confusion about why we are not following other universities in the region who I think moved online earlier, pre-empting this."
Meanwhile a lecturer at the university, who said she had spoken to a colleague who felt face-to-face teaching was unsafe, told the PA news agency: "I had to remind her we are not working on the railway lines, on oil rigs or other extreme circumstances.
"We shouldn't be in a situation where we don't feel safe at work - nobody should."
Staff were informed of the scale of the outbreak in the university by email. “It's terrifying” the lecturer added "and that information was delivered in a way that did not recognise that we would see that figure and gasp in horror".
Jo Grady, general secretary of the University and College Union, urged the government and university officials to tackle the unfolding crisis of case spikes in learning establishments “immediately”.
She said: "We warned last month that, given the current restrictions in the region, the direction of the infection rate and the problems with test and trace, it was clearly far too soon for a mass return to campus.
“We told Northumbria University they had a civic duty to put the health of staff, students and the local community first and we take no pleasure in now seeing another preventable crisis play out.”
Meanwhile councillor Irim Ali, Newcastle City Council's cabinet member for neighbourhoods and public health, blamed a “small number of students” who she said were “undermining” efforts to bring the outbreak under control.
She said: “We are working alongside both universities to support those students who are self-isolating, and have mobilised volunteers to deliver food packages and other essential items to those confined to their accommodation.
“But while work continues to control ongoing outbreaks, we need all students to comply with the regulations and guidance.”
However some students have argued the examples set by rule makers undermine measures designed to curb the spread of the virus.
Ewan Hillier, a film and TV production student at Northumbria, said: “There are accommodations with hundreds of students in and some are not following the rules and mixing ... so I am not surprised by the cases.
“When you see MPs breaking the Covid rules such as Margaret Ferrier or the bars in parliament open after 10pm ... We are young adults who follow what we are told and when rules are unclear and the leaders break the rules themselves how do they expect us to follow them?"
He added that he was still waiting on results from a test he had taken five days prior, and is isolating as his flatmate tested positive on Saturday.
"I am annoyed that the uni told us to come back," Mr Hillier said. "Most students have and are in contracts with accommodations for the year when I could have stayed at home, been safe and not wasted money."
A spokesperson for the Northumbria Students' Union said it had been working with the university and council to “create an environment where students can not only safely access the education they came here for but enjoy life on campus too”.
“We've adapted the use of our buildings and the services we provide to ensure that students enjoy a great start to their university experience, whilst taking every precaution to limit the spread of the virus,” they added.
Additional reporting by PA
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