Mr Hancock said the government was “expanding eligibility for testing further than ever before”.
He added 100,678 tests had been conducted on Sunday.
Testing in England and Scotland has been limited to people with symptoms who are key workers and their families, hospital patients, care home residents, over-65s and those who need to leave home to work.
In Wales and Northern Ireland it was just key workers, hospital workers and care home residents.
One particular concern is that the app does not yet let users know if the person they have had contact with ends up testing positive. Instead, it has only let them know if the contact has developed symptoms.
That is a major problem. It means people have been left in limbo and incorporating that feature into the app will be important.
Progress is being made, but getting a workable and efficient system in place soon is still a monumental challenge.
Mr Hancock also said the government is in the “closing stages” of negotiations to purchase new Covid-19 antibody tests.
A test developed by Swedish pharmaceutical company Roche was approved for use by Public Health England last week.