Family historians the world over will be familiar with this church because from 1837 to 1933 one of the General Register Office's main Civil Registration Districts in London for recording births, marriages and deaths was named after it.
The Church itself was built between 1721 and 1724 at a cost of £10,000, having been ordered by an Act of Parliament in 1711 to create 50 new churches in and around the expanding areas of London. The architect was John James, one of Sir Christopher Wren's assistants. The church is not actually in Hanover Square, but a block away to the south at the junction of St George Street with Maddox Street. The Church's website is here Link
Berkeley Square was laid out as a garden in 1698. Lord Clive lived on the west side at No.45. It has some magnificent plane trees planted in the mid-18th century. See more at http://en.wikipedia.org/wiki/Berkeley_Square