A city-wide fundraising drive is under way in Liverpool after a unique baby hospice which has supported thousands of families in the region was threatened with closure.

Zoe’s Place, a charity that cares for children with life-limiting conditions from birth to the age of five, announced that it had just weeks to raise the £5m needed to fund a new building, with the lease on its current site set to expire.

People in the city, many of whom have had family members or friends cared for by the centre, have thrown themselves into collective fundraising efforts which have already resulted in half of the total amount needed being donated in a matter of weeks.

Supporters have taken on physical challenges such as walks and runs, and social media pledges in efforts to save the charity.

Their support has been matched by pledges from local celebrities including former Liverpool FC footballers Steven Gerrard and Jamie Carragher, and actor Claire Sweeney.

Liverpool football fans held up a “Save Zoe’s Place” banner at Anfield before the club’s game against Chelsea on Sunday, after raising £150,000 for the hospice.

“The support has been astonishing,” said Summa Gill from the charity. “Because [Liverpool is] a big place and because it’s such a loyal and committed and compassionate city, we are just absolutely blown away by the support we’ve seen. To get this kind of support is the stuff of dreams.”

The charity is a much-needed lifeline for families in Merseyside and the surrounding areas. The centre is one of only three baby hospices in the UK which support children with life-limiting conditions from birth to the age of five, in some cases offering end-of-life care.

About 50 families are supported by the Liverpool service each year, with two other hospices in Middlesbrough and Coventry.

The charity’s head of fundraising, Matt Meaney, said: “If we lose this service, some families won’t have access to the same level of care. They may well get some respite in other hospices but it will be probably less, and some of the children who don’t meet the criteria for other providers might not get any care.

“So this isn’t a case of an inconvenience for families, the genuine situation would be that if we closed, some families will lose access to respite care.”

Steph Perry said the charity has made a “big difference” for her three-year-old daughter Robyn, who has spina bifida and cannot be looked after in a conventional nursery because of her needs.

“I’m getting upset,” she said as she spoke about what would happen if the hospice closed. “I’d be devastated, because it’s literally our home from home, and it’s a lifeline for all the children.

“The babies and children don’t deserve to lose it, because there’s nothing else in Liverpool so I’d have nowhere else to take her, so she’d have nowhere.”

Its current home is owned by the Institute of Our Lady of Mercy, a Roman Catholic order which plans to sell the land and served notice on the hospice two years ago.

The order extended the charity’s lease until June next year and waived the rent in order to help keep Zoe’s Place running. Though planning permission has been granted for a new building on another site, it may have come too late.

Costs have almost doubled from the initial plan, from £3.5m to £6.4m, with the price of raw materials and the cost of labour having soared. A total of £1.7m of match-funding has been secured but is only available if the rest of the money is raised.

The charity was founded in Liverpool in 1995 by Prof Jack Scarisbrick, with the name chosen because Zoe means “gift of life” in Greek.