A senior Tory minister has admitted that the government is likely to miss its own target for 100,000 daily tests for coronavirus by the end of April.
The deadline for hitting the target passed on Thursday but a time lag in reporting results means it will not be known until Friday whether the target was met.
Health Secretary Matt Hancock is due to deliver an update on testing later, Mr Jenrick said.
The latest testing figures show that in the 24 hours to 9am on Thursday, 81,611 tests were carried out against a capacity of more than 86,500.
Mr Jenrick told Sky News: “I think we will either have met it or be very close, and in that sense the target will have succeeded because it will have galvanised people across government, in the private sector and across the country.
“This in itself is just a stepping stone; we need to go beyond 100,000, but we have seen now a very substantial increase in testing in quite a short period of time, so in that sense it’s been a success, but there’s more to be done.”
Mr Jenrick also told BBC Breakfast there is a definite need to increase testing past 100,000 per day – seen by many as a key route out of lockdown.
Regarding face masks and face coverings, the minister said the evidence showed they offer “modest benefits” but they might “be a way of giving us all more confidence in going about our business in a safe way”.
Following an indication from Prime Minister Boris Johnson on Thursday that the guidance on face masks will change, Mr Jenrick added that a mask “does not make a huge difference but it might make some”, saying they may help people feel safer going to work.
It comes as a BBC poll of 1,000 people found that more than 60% would be uncomfortable about going out to bars and restaurants or using public transport should ministers decide to relax the lockdown.
More than 40% would still be reluctant to go shopping or send their children to school and more than 30% would be worried about going to work or meeting friends.