White Conduit House started life in the late 17th century as a tea garden where city dwellers could escape for the grassy fields and relatively clean air of Islington. According to Oliver Goldsmith it was a site where "the inhabitants of London often assemble to celebrate a feast of hot rolls and butter". For over a century from the 1750s to the 1850s the curved front of White Conduit House and its pleasure gardens hosted not just cricket matches played on White Conduit Fields to the North West, but a wide range of entertainments of all kinds, as illustrated in the images below. A good account of White Conduit can be found in British History Online, here.
Update, December 2019. Little Georgia Restaurant, at No 10 Penton St where it meets Dewey Road, is inscribed "White Conduit House" at the top - see processed photo below. Clearly it is not the original building, but it marks the site, which we can confirm using a screenshot from the excellent Layers of London website, where a Greenwood map of 1828 is superimposed on a street map from today. The gardens to the East behind White Conduit House presumably formed part of the facility. They are now for the most part occupied by buildings between Tolpuddle St and Dewey Rd, although the South part of Culpeper Gardens is still evidence of the gardens today.
Update, February 2022. As mentioned elsewhere in this website, White Conduit Fields was the birthplace of the MCC, owner of the Lord's cricket ground. Richard from Cloudesley Square has unearthed this entertaining account of how a Mr Thomas Lord was responsible for this development, apparently actually physically moving the turf via a number of sites before establishing the present day Lord's in St John's Wood.