Care for the Family has expressed its support for the National Childbirth Trust's new scheme, which seeks to award chains with "parent-friendly status" if they agree to implement certain measures in their shops.
The coffee chain Starbucks is the first to be awarded the status, and introduced new procedures in its stores on Thursday.
What 'parent-friendly' stores offer:
A place where you can feed your baby or toddler in comfort, knowing staff will support you without judgment;
Help from staff if you need any assistance, for example help finding seats or carrying, and;
An open and responsive approach to feedback.
Caroline Bradley, from Care for the Family said, while it may be difficult for stores like Starbucks to implement parent-friendly practices because of space or business, the scheme was a move in the right direction.
Mrs Bradley, who recently became a grandmother herself, also said it is much easier now for parents with newborn babies or young children to go out-and-about on the high street than it was when she became a mother decades ago.
She told Premier's News Hour: "I think it's absolutely integral to society. Mums and Dads are raising the folks of tomorrow who're going to look after our world, look after hospitals and schools and our communities.
"Going out with Mum to do everyday life is how children learn to socialise, how they learn to be safe. It's an education for them every time they go to the supermarket.
"I think it's really, really important that we are a society that's welcoming and warm and safe for children and mums and dads."
In a statement, Starbucks said: "We want all of our customers to have a good experience at Starbucks and we recognise that parents out on their own with very young children, sometimes for the first time, appreciate some support.
"Our collaboration with NCT and its members builds on our existing customer service principles and, through working with NCT, we have already refreshed our training and improved our facilities.
"We hope parents of young children visiting our stores will let us know, there and then, if there is anything we can do to improve their experience. We welcome feedback as this is just the start of an evolving collaboration with NCT and its members."
Listen to Premier's Aaron James speaking to Caroline Bradley on the News Hour: