Foyezur Miah, head of the Queen's Crescent Community Centre in Camden, said he had been told the council had a 3.5m pound hole in its Sure Start budget - a claim the London borough denies.
But Miah and Mick Farrant, chair of the centre's board of directors, are still waiting to hear if they will get a £40,000 grant from Sure Start to fund services for the coming year.
If they do not get the money, which they applied for back in November, then the centre, which also provides youth and community services, could have to stop its work.
"We don't even know when the decision will be made," Farrant said. "Staff are aware of the situation and we're not trying to panic them but they could choose to go elsewhere. If we don't get the money we will have to stop the whole programme."
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