Robert Jenrick told Sky News that Thursday's figures would be released later today, and he was hopeful of a huge ramping up in the final day of April.
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Health Secretary Matt Hancock set the ambitious target earlier this month as part of a promise to increase the numbers of tests being done.
He has expanded the criteria meaning that 25million NHS staff, key workers and others who need to leave the house to go to their job can now get a test.
Yesterday Boris Johnson revealed that the country was 20,000 short of the target, and had tested 81,000 on the second to last day before the target had to be met.
The Housing Secretary said: "I think we will have either met it or be very close."
"In that sense the target will have succeeded because it will have galvanised people across government, in the private sector and across the country to build the network that we needed to, which is the foundation of testing, tracking and tracing, which we need in the next phase of fighting the virus."
He added: "This in itself is just a stepping stone.
"We need to go beyond 100,000, but we have now seen a very substantial increase in testing in quite a short period of time.
"In that sense, it's been a success. But there's more to be done."
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Grant Shapps echoed the same words last night, telling BBC Newsnight: "At the beginning of the week we only had 5,000 home tests available, we now have 20,000 available and it's the reason we are quite likely to get very close to or meet the 100,000 target."
Home testing kits have been flying this week, with ministers releasing nearly 15,000 a day direct to doorsteps.
A Government source also told the BBC they were "fairly confident" that testing numbers "will be where our projections forecasted them to be".
"But you can never take anything for granted," they added.
Testing is seen as being the first stage of a plan to end the lockdown.
More testing will be set up, followed by an extensive track and trace programme to target anyone who may have been in contact with the killer bug.
Boris Johnson tweeted this morning an appeal for Brits to stay on track and work together to beat the bug.
He said: "I can confirm that we are past the peak of this disease.
"We are past the peak and we are on the downward slope.
"And we have so many reasons to be hopeful for the long term.
"But we can only defeat coronavirus by our collective discipline and working together."
Britain is recruiting an army of tracers at the moment to form part of a huge ten, expected to be in the tens of thousands.
Chasing down people that new sufferers have mixed with to halt contagion chains has proved hugely successful in countries like South Korea and Germany.
But for track and trace to work, ministers believe the number who currently have the virus will need to be reduced to 100,000 first, The Sun can reveal.
At the moment, the estimated number is still running at 350,000, according to the King’s College London tracker.
Without the track and trace scheme in place, it is likely the Cabinet will decide the full lockdown will have to stay in place beyond the next review point on May 7.
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