Speaking on the programme this morning (Thursday, March 12), Dr Hilary said the UK Government should have put a ban on large gatherings in place weeks ago - and claimed Britain could face a mass lockdown as a result of the escalating outbreak.
Italy, which currently has lockdown measures in place, is the worst hit country in Europe and the second worst hit in the world, after China.
So far, it has seen over 12,000 cases and more than 820 deaths.
As of Thursday afternoon, the UK had a death toll of 10 against 590 cases of the flu-like bug.
Clearly this is very serious.
And with Prime Minister Boris Johnson holding an emergency Cobra meeting this afternoon to discuss the move into the 'delay' phase of the Government's strategy to tackle the spread of the virus, Dr Hilary pointed out that lockdown measures should have come earlier.
He explained: "We were always running containment and delay concurrently in reality. We always knew numbers were going to increase, probably double, every three to four days.
"We are on the same trajectory as Italy. If you look at the Italian situation, overnight two hundred deaths nearly, so clearly this is very serious.
"Having said that, the delay phase is critical. People need to socially distance. We should have banned these mass gatherings probably a week ago."
Speaking further, Dr Hilary pointed out that events like the Cheltenham races, which are being held this week, should have been cancelled.
That opinion echoed calls from GMB host Piers Morgan, earlier this week, for people to put the health of Britain's elderly and most vulnerable ahead of the need to have a good time.
The presenter was discussing Cheltenham Festival with his co-hosts Susanna Reid and Charlotte Hawkins when he said: "The health of our elderly and those who've got underlying health conditions should be more important than all of us just going about having jollies."
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