It comes after the Government's scientific advisers reportedly decided that students should be kept in isolation at universities over the festive period.
And Dr Hilary said on Good Morning Britain on Thursday that he agreed with the reported advice.
"There’s not a lot of good news is there, certainly university campuses [are] likely to be where transmissions are rife," he told hosts Susannah Reid and Ben Shephard.
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"When those students come home to all parts of the country, it’s like lots of different households mixing together in close contact.
He added that "if you look at it in the cold light of day, it makes sense, scientifically, to keep those people who are likely to be transmitting more separate from [people who are likely to be] more vulnerable".
Minutes from the latest meeting of Sage, the Government's scientific advice group, are expected to say that the risks of major coronavirus outbreaks “spilling over from HE institutions” are more likely to take place as the academic term comes to an end, coinciding with Christmas and New Year, inews reported.
“This could pose a risk to both local communities and families, and will require national oversight, monitoring and decision making,” Sage will warn.
It comes as universities across the UK are already struggling with outbreaks at the start of the new term.
Liverpool University has said 87 people have tested positive this week. The University of Dundee has told 500 people to self-isolate after a number of cases in its halls of residence. Glasgow University has also been hit by an outbreak with 124 students testing positive.
A Department for Education spokeswoman said: “We will continue monitoring the situation very closely and follow Public Health England advice, adapting policies to best support students and providers as the situation evolves.”