Government chiefs made the call to allow people subject to tighter rules to look after children from other households.
The restrictions – banning the mixing of households – were imposed across Wolverhampton, Birmingham and Sandwell amid a surge in virus cases.
But, after a string of complaints from parents, Health Secretary Matt Hancock reversed his decision – meaning children under 14, or vulnerable adults, will be exempt.
It means grandparents living in the affected areas will be able to see their loved ones if they are caring for their family members.
A spokesman for Sandwell Council said: "We welcome the help this will provide to Sandwell families with childcare and we await the full guidance on this from the Government.
"We would remind everyone that, under the Government’s restrictions for Sandwell, people who don’t live in the same household must not visit each other’s homes unless they are specifically looking after children under the age of 14 or because of other essential reasons outlined in law by the Government.
"Infection rates remain high in Sandwell and household transmission is one of the key ways the virus is being passed onto others. So please follow the rules and all the advice to keep yourself and your loved ones safe."
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Grandmother Andrea Manns, who lives in Darlaston, said she wouldn't be affected by the move but described the situation as being difficult.
She said: "I'm in Walsall so I'm able to see my granddaughter, but I can't see my mother and great-great nan because they live in Sandwell.
"It's just a bit confusing again and it's a shame because of the restrictions being introduced means I can't see my family.
"I'm not sure what's going on and it's been really hard for the family – you're not sure if you're doing the right thing, if you're in a social bubble or not.
"My granddaughter has been coming round just to me at the moment and it's just been very difficult."
Councillor John Reynolds, Wolverhampton Council's cabinet member for children and young people, said: "We welcome this announcement which will come as a welcome relief to families who rely on others, whether they be relatives or friends, to help them look after a child or vulnerable adult.
"It's important to stress that this must be a continuation of existing arrangements, so if a friend or relative has been picking up a child from school or looks after a little one while their parents are at work, or if someone looks after a vulnerable adult or child, this can continue.
"If it is not an existing arrangement, the rules around households remaining apart should apply – that means you must not invite anyone into your house or garden if they are not part of your household, support bubble or care bubble, and nor should you visit other people’s homes or gardens. One-offs such as play dates are not permitted.
"We all need to follow the guidelines and do our bit to stop the spread of coronavirus and we must not lose sight of the fact that Covid-19 poses a greater risk to older and more vulnerable people. Forming a care bubble should only happen if absolutely necessary, and I would urge people who are more at risk, like grandparents, to carry on doing all they can to minimise their exposure to the virus as much as possible."
The move has been welcomed by councillors in Birmingham – another area where the restrictions had been imposed – who wrote to the Health Secretary over the issue.
Birmingham City Councillor Robert Alden said: "It was simply wrong that those who could afford a nanny could continue to get childcare but those who relied on relatives could not.
"This commonsense change will be a relief to thousands of families across Birmingham and we very much welcome this change."
Mr Hancock, during a speech to the House of Commons, said he made the changes after concerns were raised over the impact on childcare arrangements.
He said: "For many, informal childcare arrangements are a lifeline, without which they couldn't do their jobs.
"I'm able to announce a new exemption for looking after children under the age of 14 or vulnerable adults where that is necessary for caring purposes.
"This covers both formal and informal arrangements. It does not allow for play-dates or parties, but it does mean that a consistent childcare relationship that is vital for somebody to get to work is allowed."