Chantal Nogbou, 43, co-founded the baby bank around five years ago.
The charity, based in the St John's Centre, supports children living in poverty across the city.
Leeds Baby Bank provides basic essentials such as nappies, formula, clothes and toys for children aged 0-5.
However, their supplies have dwindled in recent months due to a rapid increase in the number of referrals for their services.
Now, Chantal has issued a rally cry on behalf of the charity to Leeds residents to help restock vital items - just weeks before the next anticipated surge due to April's energy bills landing.
"Our numbers have been going up every single month", she told the YEP.
"We are struggling to fill our shelves.
"As soon as stock is coming in, it is going out."
Chantal said pre-Covid, the charity would help around 60 families a month on average.
The Covid pandemic - combined with the rising costs of bills - has now left the charity supporting more than 200 vulnerable families from across the city.
Chantal said "a whole new kind" of service user has been created recently due to the financial burden on families in Leeds.
"People are suddenly struggling", she explained.
"The people who used us before are in higher need than ever but there are also families using us for the first time.
"Many were just about managing but have then been told about the new bill prices.
"Where are they expected to get that extra money from?"
Almost half of adults were struggling to pay their energy bills before the biggest jump in prices in living memory came into effect this week, figures suggest.
Some 43 per cent of adults in Britain who pay energy bills said they were finding this very or somewhat difficult in March, according to the Office for National Statistics (ONS).
With the cost-of-living crisis continuing to bite, six per cent of those with gas or electricity supplied to their homes said they were behind on these bills.
The stark findings reveal the struggles people were experiencing even before Friday’s hike in the energy price cap.
For families using Leeds Baby Bank, times have never been tougher.
On Thursday mornings, the tour offers an outreach service within communities.
"We have about 40 families come to that each week and pick up the essentials, nappies and things like that", Chantal explained.
"There is a never ending wish list."
Chantal said the stock at their unit in St John's Centre Leeds is constantly being given out to families and anticipates demand only increasing.
She added: "People are asking us if we have any baby baths, as they are cheaper to fill than a full size bath.
"With inflation and the rising cost of bills, the increase in benefits has not matched up.
"It has left everyone struggling."
Chantal said the baby bank were happy to support Ukrainian refugees recently.
She said: "It was obviously not something we had prepared for.
"They have left their country with nothing.
"We were asked to help out by the council and sent out some of our stock to help."
Chantal has asked Leeds residents to help support the baby bank in the coming months.
"We are expecting a surge", she said.
"There are some items we are very short of."
To find out ways to donate, click here.An Amazon wish list has also been set up to provide an easy way to support the charity's work.
The full list of items Leeds Baby Bank is requesting is as follows:
Prams - especially doubles
New baby bottles
Clothes - up to the age of five
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