The Health Secretary said that it appeared that there were “credible cases” of reinfection.
But he also seemed to hint that the numbers of people getting coronavirus twice may be low, that the subsequent infection may be less dangerous and not as infectious.
Scientists were urgently seeking to find answers to these crucial questions.
After reports of a small number of cases of individuals getting Covid again, Mr Hancock told LBC Radio: “The scientists in the department are looking very closely into it.
“But it does appear that these cases of reinfection are credible.
“The question is how many there are and also how dangerous it is if you catch it again, and how infectious you are if you catch it again…as in do you get just a much, much smaller dose.
“There is a lot of very important scientific questions that we are doing a huge amount of work into trying to understand it from the relatively few number of cases that we have seen so far.”