I've just answered my own question. According to Genuki:
The majority of historical church records for London and Middlesex are held by four repositories:
•London Metropolitan Archives hold records for most Anglican parishes in Middlesex, though the registers for a few ancient parishes have not been deposited, and some are elsewhere. They also have a wide range of 19th and 20th century non-conformist records. All registers held at LMA are listed on the London Generations Database.
•Guildhall Library holds records for most Anglican parishes in the City of London, and some of the Middlesex parishes that adjoin the City.
•The City of Westminster Archives Centre holds records for most Anglican parishes in the former Metropolitan Borough of Westminster (corresponding to the southern part of the current City of Westminster), though some from this area are not deposited and others are at LMA.
•The National Archives hold registers from non-conformist and non-parochial Anglican churches and chapels surrendered to the Non-parochial Registers Commissions of 1837 and 1857.
•The Westminster Abbey Library & Muniment Room holds records for a few Anglican churches in Westminster.
