Restrictive lockdown measures could be re-introduced in areas with "flare-ups" of the pandemic, Government officials have said.
It comes after the West Midlands was branded a "hotspot" at the start of the fight against the virus – with the death toll since hitting more than 2,350.
Health Secretary Matt Hancock said any decision would be made by the Government using advice from health experts.
Stuart Anderson, MP for Wolverhampton South West, said the country was in "uncharted territory" when it came to lifting restrictions.
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"If the Government decides to do a local lockdown in specific areas then it will be based on the best scientific advice," he said.
"It's far better than the whole country being locked down, but we're coming out and things are starting to open up again.
"But we're in uncharted territory and so step by step we have to ensure we are preserving life – and I would support a local lockdown if it meant saving lives."
Mike Wood, MP for Dudley South, said different measures might be needed in certain areas, but he hoped it didn't happen in the Black Country.
He said: "In the Black Country we have seen some really good trends in the reduction of infections, hospital admissions, deaths falling from Covid-19 in the past few weeks.
"That is thanks to people taking care when they go out – and not going out when they don't need to.
"Obviously, if infection rates picked up, we can step up some restrictions but none of us want to.
"The most important things is saving lives. If some parts of the country – we hope, pray and we want to make sure it doesn't happen in the Black Country – suddenly have higher infection rates than others then different measures will be needed to the rest of the country."
John Spellar, MP for Warley, said the country needed to get back onto its feet as he welcomed the measures.
He said: "It is essential that we get the economy and society moving again.
"Obviously we have got to have a back-up if we get a spike, like other countries have done.
"I have seen quite a few countries, like China and South Korea just recently. In one town they had a problem and therefore took action."
Eddie Hughes, MP for Walsall North, said a region-wide lockdown – if needed – would help other areas with lower rates continue with eased restrictions, rather than the whole country being locked down.
"We're a pragmatic bunch in the Black Country and it's important we don't end up in a position where there's too many cases and it overwhelms our NHS," he said.
"If a regional lockdown is necessary, it's probably a good idea – a very good idea – as those areas who have lower R-rates (rates of infection) can continue with eased restrictions."
Michael Fabricant, MP for Lichfield, said he supported the measure but said it could be difficult to monitor people moving from place to place.
He said: "It's now getting to the stage where local lockdowns may be necessary, but I'm not sure how we will enforce them, in particular, the movement across local government areas. But clearly, there are growing differences between different parts of England and the UK as a whole, so local lockdowns do make sense."