Mr Hancock said he was confident the country was at the peak but stressed that continued social distancing was needed to bring the number of new cases down.
He told MPs, many of whom joined the Commons session remotely: “We are ramping up our testing capacity and our capacity for contact tracing in a matter of weeks.”
Shortly afterwards, the Department of Health said 18,100 patients had died in hospital after testing positive for coronavirus in the UK, as of 5pm on Tuesday, up by 763 from 17,337 the day before.
Scientific experts and former health secretary Jeremy Hunt have pressed the Government for more details on mass testing and contact tracing, which is a key route out of the UK lockdown.
By finding those who are infected with coronavirus and tracing their contacts – and isolating both – routes of onward transmission of Covid-19 can be slowed until a vaccine is found.
Mr Hancock told MPs the expansion of testing capacity “was ahead of plans” and the number of people eligible for testing was being expanded.
“And as we have reached the peak, and as we bring the number of new cases down, so we will introduce contact tracing at large scale,” he said.
However, the latest Government figures showed less than half the testing capacity was used in the 24 hours up to 9am on Tuesday.
Capacity stood at 41,398 but only 18,206 tests were carried out over the period in England, Wales and Scotland.
Mr Hancock said the Government was working “closely with some of the best digital and technological brains” on the contact tracing app, which is in trials.
He said: “The more people who sign up for this new app when it goes live, the better informed our response will be, and the better we can therefore protect the NHS.”
Asked what the current level of Covid-19 was in the general population and when test, track and trace (which includes contact tracing) could be brought in, Mr Hancock said: “The current level of incidence is unknown until we expand testing further. But it is far, far higher than where it needs to be, though we are at a peak.
“We have high confidence that we are at a peak in this disease, but obviously we need to see that come down. It’s a question of degree.
“The fewer new cases, the more effective test, track and trace are as a way of keeping the disease down, and therefore the more of the social distancing measures can be lifted.”
He stressed that the Government was working to build the “capacity for that very large style contact tracing”.
He agreed that contact tracing professionals would need to be used for test, track and trace alongside the app, adding: “That way we can control this virus, with fewer of the very extraordinary social distancing measures that have been in place.”
Mr Hancock said the NHS would resume treating patients with a wider range of conditions soon following fears that thousands of people are dying or seeing serious conditions, including cancer, go undetected.
He said: “We want to reopen the NHS to non-coronavirus symptoms and to patients with non-coronavirus conditions safely and carefully, as soon as it’s safe to do so. But the first step that we’re taking is to send the message loud and clear to people who have suspected conditions that they should come forward.
“If you think you might have a lump that might be a cancer, then you should come forward now, and you will be safely and properly treated in the NHS.
“The same goes if you have a suspected heart attack or stroke – we have the systems in place to make sure that if you come to the NHS, you will be looked after and protected.”
He said the Government was working to “gradually reopen the rest of the NHS” to other procedures, including non life-threatening, planned surgery.
The Government was also looking at why the death rate as a proportion of the population is lower in Germany than in the UK “as we try to learn”, he said.
It comes after Dominic Raab faced a grilling in his Prime Minister’s Questions clash with Sir Keir Starmer.
The new Labour leader and Foreign Secretary Mr Raab – deputising for Boris Johnson as the Prime Minister continued his recovery from Covid-19 – faced each other in a sparsely attended House of Commons.
Sir Keir questioned the Government’s progress towards its target of 100,000 tests a day by the end of the month and claimed that opportunities to acquire personal protective equipment (PPE) from British firms had been missed.
He said: “There is a pattern emerging here. We were slow into lockdown, slow on testing, slow on protective equipment and now slow to take up these offers from British firms.”
Mr Raab told him the Government was guided by scientific advisers.
He said that if Sir Keir “thinks he knows better than they do, with the benefit of hindsight, then that’s his decision”.
Mr Raab said 8,000 British businesses had responded to a call for assistance on PPE and they had all received a response, with 3,000 followed up where it was “sensible” if they had equipment with the required specification and volume.
He said it was an “incredibly difficult and competitive international environment” to source PPE from overseas.
Mr Johnson continues to recover from coronavirus at Chequers and Mr Raab said the Prime Minister was in “good spirits”.
In other developments, an RAF plane landed at Brize Norton from Turkey in the early hours of Wednesday, after being sent to collect a shipment of PPE.
The Government also continues to face questions about its participation in EU schemes to secure vital equipment, with Brussels saying there had been “ample opportunity” for the UK to join in.