The new cases in the city were confirmed this afternoon as the the Chancellor promised the NHS “whatever it needs” in terms of funding to tackle the spread of the virus in his Budget statement.
Rishi Sunak set out plans for the health service in his Budget and pledged security and support for those who are sick and unable to work due to the spread of Covid-19.
Wolverhampton Council leader Councillor Ian Brookfield called for calm as he laid out the authority's plans to deal with disease.
Cars were being directed onto the testing centre, off Showell Road near Stafford Road, just outside the city centre after it was set up opposite KFC yesterday.
Meanwhile customers stockpiling essentials have left shelves empty for other shoppers in the Black Country, with the owner of a Tipton cash and carry describing having to stop customers stealing from each other's trolleys.
And a primary school in Walsall has shut for three days for a deep clean after staff reported having flu-like symptoms.
More on coronavirus
Prior to the Budget announcement this afternoon, the Bank of England lowered interest rates from 0.75 per cent to 0.25 per cent to counter the “economic shock” of the outbreak.
Health Minister Nadine Dorries became the first MP to be diagnosed with Covid-19, but there are no plans to test any ministers, including PM Boris Johnson.
In sport, Wolves players and backroom staff were preparing to fly out to Greece for the club's Europa League match with Olympiacos after the club's appeal for a postponement was rejected by UEFA last night.
WATCH:Test centre up and running
People in the city who display symptoms of Covid-19 and call NHS 111 are being told not to attend New Cross Hospital or their GP.
Instead they will be directed to the car park test centre.
Motorists are asked to pull onto the site before swabs are taken.
In most cases, patients will know within a day whether they have been infected, with the confirmed cases being urgently prioritised.
Visits to the test centre are by appointment-only and people must have been referred by NHS 111.
The centre was the first of its kind set up in the Black Country.
Sandwell health officials revealed they were in talks to establish the borough's own site, with the NHS in England planning to “ramp up” testing facilities so that 10,000 coronavirus tests can be performed each day.
So far more than 25,000 tests have been conducted by public health officials in England but it is hoped that within weeks 10,000 swabs will be assessed each day.
A Walsall Council spokesman said the authority had "advanced plans" to introduce a test centre similar to the one in Wolverhampton "ready in the event that the number of tests required increase."
At present, diagnostic facilities can perform around 2,000 tests a day across the country but the NHS announced it was undertaking a “significant expansion”.
Professor Dame Sue Hill, NHS chief scientific officer, said: “The NHS is ramping up the number of testing centres across the country, to help people get care quickly or have their mind put at ease.
Council will prioritise key services
Wolverhampton Council leader Councillor Brookfield says the authority is looking at its contingency plans.
"It looks like we're going to have to bunker down for a few months as the epidemic takes hold," he said.
"If this goes the way that the experts are saying we will see a difference in the way the council operates.
"We will quite rightly prioritise meals on wheels and waste collection, and as with organisations all over the country, there are some jobs where we will be asking people to work from home.
"The fact of the matter is, coronavirus is in our city."
He added: " We don't have to go crazy and isolate for six months, we are probably talking a couple of weeks. There's no need for people to rush out and buy half of Tescos."
He also urged people to keep an eye on elderly neighbours. "Everyone's priority is to look after those people in their communities who are more susceptible to becoming ill," he said.