The Transport Secretary warned that just because some of the data looked encouraging did not mean that it would carry on.
Death and case numbers are expected to continue to rise in the coming days and weeks as the UK gets near the peak.
Mr Shapps told BBC News: “There is a long way to go.
“I know people are seeing two or three days of the chart coming down but I don’t expect that to continue.
“We are not at the peak yet and it is really important we continue following this advice.”
All Brits have been told they must stay at home unless essential – such as going out for food or medicine.
And one exercise trip per day is allowed too.
But no one should be meeting anyone outside their households unless they absolutely have to, the Government has said.
Strict fines are in place for people gathering in groups of more than two in public.
Boris Johnson told Cabinet today – which was done via videolink – that it would get worse before it gets better.
A No10 spokesperson said this morning: “The PM said the rising death toll in recent days showed the vital importance of the public continuing to stick to the social distancing guidance which has been put in place by the Government, based on scientific and medical advice.
“The message to the public is: Stay at home, protect the NHS, save lives.
“The PM said that the situation is going to get worse before it gets better – but it will get better.”
Last night health officials revealed data on the lockdown shows positive signs of working.
Chief scientific advisor Sir Patrick Vallance said the strict new measures introduced last week appeared to be having the “effect desired” in the government’s daily press conference.
He revealed the glimmer of hope as he told the nation: “The measures are in place, they are making a difference, they are decreasing the contact which is so important to spread the disease and we’re doing a good job at cutting that down.
“What you can see is there’s been an increase in the number of cases since the middle of March through to today.
“We expect that measures that are in place that cause that social distancing, the stay at home message will be reducing the number of cases of transmission in the community and decreasing the number of cases overall.”
Train use is now down to just ten per cent of normal, bus use down to a fifth, driving to less than a third, while the London Underground is carrying only five per cent of its normal passengers.
But Sir Patrick warned that it would take two to three weeks for this to feed through to a fall in cases and hospital admissions – exposing how vital it was for Brits to continue complying with the strict order to stay at home.
He said: “Roughly 1,000 a day [admissions]… that’s not an acceleration. It’s quite important, it tells you that actually this is a bit more stable than it has been.
“The measures we are taking will stop the transmission, delay the transmission, reduce the amount of transmission in the community and therefore reduce the number of people who might die from the infection.
“I want to thank the people in the NHS working extremely hard.”
“What all of us can do is heed the advice and stay at home so we can reduce the number of people who will be seriously ill or die from this infection.”
He warned the number of deaths from the virus are expected to jump tomorrow as figures including those who have died outside of hospitals will be released for the first time.
Earlier an extra 40 deaths from outside hospitals were revealed – and more jumps are expected.
Regional data released showed all areas outside of London had steady increases in hospital admissions but were not spiking, giving more time to get ready for extra cases.
Three regional hospitals in London, Birmingham and Manchester are in the process of being set up to help deal with cases.