More than 2,000 people received Covid-19 tests at an emergency centre set up in Middlesbrough over the weekend.
A case of the South African strain of coronavirus was confirmed on Friday in the Marton and Coulby Newham areas of the town.
Health officials established a testing site at the Parkway centre in Coulby Newham to help trace any further cases.
Due to unprecedented demand, the centre temporarily ran out of tests on its opening day – but received extra supplies quickly.
Latest figures show Middlesbrough has one of the highest rates of coronavirus in the country. The town is in the top five worst-affected areas by population.
Andy McDonald, Labour MP for Middlesbrough, said the high rates were linked to poverty and deprivation.
Where you have indices of poverty and deprivation it mirrors exactly the incidents of Covid outbreaks so that tells us something much more fundamental about our economic settlement in places like this, and that has to be addressed.
Simon Clarke, Conservative MP for Middlesbrough South and East Cleveland, said: "It is at the moment only one case and we want to keep it that way."