Workers in the sector say they are worried their workplace is unsafe.
Online petitions have been set up to demand the closure of nurseries if additional support is not provided.
In the first lockdown, the government closed all nurseries, but this time they are open in England and Wales.
Ministers insist the risks are low, with nurseries providing essential support to working parents.
But the owner of the nursery, Alex Quist, says she feels “forgotten” and would rather close than stay open.
“It is impossible to distance oneself socially with this age. They need hugs, close contact. We change their diapers throughout the day, ”she says.
Like many other nursery providers, she is not convinced that early childhood settings are safe and believes that nurseries are often overlooked, unlike schools and colleges.
Nursery, Liam Thompson, caught COVID and spent Christmas in bed.
“Me and a few other staff, we caught it at the nursery, we went from child to parent and it spread pretty quickly,” he said.
Liam says procedures were carefully followed but the virus spread “faster than we could control.”
He is so worried about safety that he has set up and an online petition demanding the closure of nurseries. Tens of thousands of people have already signed it.
Nurseries have been closed in Scotland and Northern Ireland.
With infection rates soaring across much of the UK, there are now wider calls to close day care centers, backed by the Mayor of London, Sadiq Khan, and the UK’s largest union , Unison.
Early childhood officials say they need to see the data and want nursery staff to have priority access to tests and vaccines.
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Early Years Alliance chief executive Neil Leitch told Sky News: “We are just saying make our environments safe and there are things the government could do to make that happen.
“First, they could give us priority in terms of testing. And they could take us up the ranks in terms of immunization priorities. ”
In a statement, a spokesperson for the Department of Health said: “Early childhood settings remain low-risk environments for children and staff and there is no evidence that the new variant of the coronavirus affects disproportionately young children.
“Keeping nurseries and babysitters open will help parents and provide essential care and education for our youngest children.