Staff are protesting against the decision and say the closure will mean they will have to give up work to care for their children.
The Child's Play nursery at Mount Pleasant, run by Kiddicare, opened in 1994 and is attended by up to 30 children.
Postal workers held a demonstration outside the nursery site in Clerkenwell to voice their opposition to the closure.
Delivery worker Angela McNaughton, who has worked at the site for 12 years, uses the nursery to care for her one-year-old daughter during her shifts.
She said, 'I'm a single parent and if I didn't have the nursery, I'd be forced out of employment.'
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