The former Christ Church Congregational Chapel building, on Llewelyn Avenue, was previously set to go to online auction with Town & Country Property Auctions.
Despite auction dates in August, September, October and December 2024, the site was withdrawn from all four.
The building had been set a fifth auction date, for April 30, but was sold prior to the auction, the auctioneer said.
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The site had been set a freehold guide price of £125,000 with additional fees, but its sale fee remains undisclosed.
The property was built in 1858 and modified with the addition of transepts in 1863.
The chapel was designed by London-based architect Joseph James and built in the Gothic style with a short-wall entry plan, integral tower and spire (which was lost during the 1970s).
It was converted into a day nursery, Bonkerz Fun Centre, in 2011.
Bonkerz continues to lease the site, while another nursery, Kiddie’s Corner, leased a smaller section until its closure in December 2024.