Video report by ITV News Science Editor Tom Clarke
At the Downing Street press conference he said the system would continue to improve and he was “confident it will be world class”.
Mr Hancock said: “Testing for the virus and tracing how it spreads is critical for containing it locally, so that we can ease the national lockdown.
“It’s by isolating the virus that we can control it and we can stop it spreading through our communities.
“In this plan to lift lockdown, Test and Trace is our radar, if you like, it helps us identify where the virus is and trace how it is spreading through the community.”
Mr Hancock did not rule out the prospect of making it mandatory to abide the the Test and Trace rules.
Some 8,117 people who tested positive for Covid-19 in England had their case transferred to the Test and Trace contact tracing system, of whom 5,407 (67%) were reached, while 2,710 (33%) were not reached.
Baroness Dido Harding, who is heading up the NHS Test and Trace programme, said the scheme had “got off to a good start”.
She said: “Given that it is still early days this is really encouraging, it means that the vast majority of people are responding positively and willingly, sharing information and self-isolating when needed.
“Our first week of data shows this partnership (between the public and the NHS) has got off to a good start but together we know there are further improvements we can make to the system.”
ITV News Science Editor Tom Clarke analyses the latest statistics and what is next for Test and Trace
Mr Hancock said the delayed contact tracing app will be brought in “when it’s right to do so”.
“As we launched NHS Test and Trace we were clear we want to embed this system and get confidence that people are following the advice that’s given by human beings before introducing the technological element.”
Originally, it was said the app could be ready for mid-May, so it is a large climb down from the government, as it not yet fit to be released a month later.
Mr Hancock reiterated the Government's message that people should not gather in groups of more than six, a statement aimed at those planning to partake in Black Lives Matter protests in the coming days.
“I understand that people want to show their passion for a cause that they care deeply about.
“But this is a virus that thrives on social contact, regardless of what your cause may be.”
Mr Hancock also denied it was dangerous to be easing the lockdown.
“No, it’s not, and the first thing I would say is I have confidence and renewed confidence with these statistics that we will get a world-class system.
“The better test and trace is the more lockdown measures we can relieve safely but I’m confident that the measures we’ve announced to be able to relieve on Saturday for the social measures and on Monday for the retail measures, they’re safe, they’re part of the plan.
“We’re coming out of lockdown carefully and safely.”
Coronavirus: Everything you need to know