The Old Meeting House has a rather exciting history: first built in 1689 in Phillip Street (as Old Meeting Street was then known), it was burnt down in the "Sacheverell Riots" on 17 July 1715. It was rebuilt on the same site, only to be destroyed almost exactly 76 years later in the "Priestly Riots" on 14 July 1791. It was rebuilt by 1794 (as seen below), and lasted until 1885 when a new Meeting House was built in Bristol Street, the Old Meeting Street site becoming part of the New Street Station development.
[I hope I've got these facts straight. There's quite a lot about this subject, both on this Forum and in wider cyberspace.]