The health secretary said there had been “a sharp rise” in the number of people who were “not eligible” applying for and getting a test.
“If you don’t have symptoms and you haven’t been told to get a test by a clinician or a local authority then you are not eligible and you shouldn’t be coming forward,” he told BBC Radio 4′s Today programme on Wednesday.
“This increase in demand for people who are not eligible is a problem and it restricts the availability of tests.”
In a separate interview with Sky News, Hancock said “about 25% of people” who were coming forward for a test were ineligible.
Sarah-Jane Marsh, the director of testing at NHS Test and Trace, on Tuesday apologised for some people not being able to get a test when they had symptoms.
It comes after a surge in coronavirus infections across the UK led the government to impose stricter nationwide lockdown measures.
From Monday social gatherings of more than six people will be made illegal. Under current rules the legal limit s 30.
It will apply to gatherings indoors and outdoors – including private homes, as well as parks, pubs and restaurants.
Hancock said the new restrictions, which will be set out by Boris Johnson in a press conference later on Wednesday, would likely remain in place for the “foreseeable future”.
Gatherings of more than six people will be allowed where the household or support bubble is larger than six, or where the gathering is for work or education purposes.
Hancock said the reason work and education were exempt was because “we need to get through this coronavirus with the minimal impact”.
He added: “But it does mean that when it comes to socialising, we are unfortunately having to put in place these rules because our contact tracing system – which is now excellent – shows that the majority of the transmission of this disease is in social circumstances.”
Exemptions will also apply for weddings, funerals and Covid-secure organised team sports, with a full list to be published by the government before Monday.
This article originally appeared on HuffPost UK and has been updated.