The search has “narrowed down to 379 households in the south-east”, the health secretary told MPs, adding: “We are contacting each one.”
He also said just 0.1 per cent of people who take tests fail to fill in a registration card, after Downing Street was unable to say the extent of the problem.
Officials have been hunting for the individual, one of six people infected with the “variant of concern” from Brazil – but the only one who provided no information about themselves.
He or she is believed to have completed a home test, or one provided by a local authority, as staff at testing centres check that contact details are submitted.
The search had triggered criticism that Boris Johnson is “complacent” about the threat posed by new variants, some of which respond less well to vaccines.