https://search.ancestry.co.uk/search/db.aspx?dbid=61711
Covers the years 1842 - 1918. I can't find out how many records there are at the moment because it doesn't come up in the Card Catalogue yet.
Also, several of the other London Poor Law databases have been updated, but I don't know whether that means that new records have been added or just that something has been corrected.