Speaking at a Downing Street press briefing on Friday, Hancock said he was "delighted" in the success of the "flat out work" of health officials to identify the missing case, reports Xinhua news agency.
The "best evidence" shows that the person has stayed at home and there's no sign there has been any onward transmission, said Hancock.
However, testing will be increased in the local area as a precaution, he added.
The latest development came after six cases of the P1 variant were found in Britain last week, but one had been unidentified as this person failed to complete the test registration card properly.
There are concerns that this variant may spread more easily, might evade the immune system, or that vaccines might be less effective against it.
The Health Secretary said the current vaccines deployed in Britain had "not yet been studied against this variant" but that work is underway to "understand what impact it might have".
"One of the most dangerous things about this virus is around one-third of those who get it don't get any symptoms at all," Hancock said.
Therefore, rapid, regular testing is a "critical part" of the Britain's response to the pandemic, he said.
Hancock also confirmed that two-fifths of Britain's entire adult population of have now been vaccinated.
The government is "on course" to offering a first vaccine dose to all adults by the end of July, he added.
London, March 6
UK Health Secretary Matt Hancock confirmed that the mystery person infected with the coronavirus "variant of concern", which first emerged in Brazil, has been found.
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