Spain and France are among the nations that have seen rates soar in recent weeks.
The Transport Secretary said Britain is at a “critical moment” as is on track to see cases on the same scale within weeks.
He urged Britons to follow all Covid-19 social distancing rules in a bid to curb the rise in infections.
He told Sky News on Monday: "We're certainly at a critical moment this morning. It is clear we're just a few weeks behind what we're seeing elsewhere in Europe.
"You only have to look at what's happening in France, particularly in Spain, and you can see that things have taken off there including, I'm afraid, deaths.
"So it is very important that we do everything we can to bear down on this.
"It's absolutely vital that people do (follow restrictions) because otherwise we're going to end up back in situations we don't want to be in."
During the past two weeks, Spain has reported more than 122,000 new Covid-19 cases, with a rate of cases per 100,000 people soaring to 259.76
France has reported in excess of 10,000 new cases per day in the past week, with 166.9 cases per 100,000 people.
In the UK, there are 59.3 cases per 100,000, with another 3,899 lab-confirmed cases of coronavirus in the UK announced on Sunday . A further 18 people died within 28 days of testing positive, bringing the UK total to 41,777.
Mr Shapps explained that the Government also expects deaths to follow.
“We're seeing the hospital admissions creeping up, albeit deaths haven't followed as yet. What we do know, looking at places like Spain, that will follow,” Mr Shapps said.
Speaking to BBC Breakfast, Mr Shapps warned of further restrictions. He said: "It's very clear when you follow the data that we need to make sure we are applying all these measures or we are at this tipping point where we may need to go further - that's something we would like to avoid.
"A debate is quite proper, that's exactly what you would expect.
"Everyone recognises there is a tension between the virus and the measures we need to take and the economy and ensuring that people's livelihoods are protected, and we want to protect lives and livelihoods."
Mr Shapps said he was briefed by chief medical officer for England Professor Chris Whitty and chief scientific adviser Sir Patrick Vallance over the weekend. The two experts are due to give a televised briefing on Monday morning while the Prime Minister is expected to announce more new measures in a press conference as early as Tuesday.
"The situation is clearly worsening," a spokesman for the mayor said.
"The mayor wants fast action as we cannot risk a delay, as happened in March. It is better for both health and business to move too early than too late."
The latest figures came after the Government announced anyone in England refusing to obey an order to self-isolate could face a fine of up to £10,000 and just days after the "rule of six" - banning social gathering of more than six people - came into force.
Sir Keir Starmer has said Labour would support any new measures but warned that a second national lockdown was becoming more likely because the Test and Trace programme was in a state of "near collapse".