Wandsworth has the lowest empty homes ratio of London Boroughs, at 1.2 empty homes per thousand. As this article highlights, this compares very favourably to other Boroughs including Lambeth (6.6), Merton (7.3) and Westminster (2.4).
The article references the availability of powers of compulsory purchase (using powers in the Housing Act 1984) to encourage reticent owners to bring properties back to a habitable standard, or indeed to deal with properties in unknown ownership, though the latter is a most likely a rare occurrence.
As alluded to, often in the case of empty homes the threat of CPO is sufficient to kick start some action. In some instances it may be necessary to start formal procedures, such as securing resolutions from members to use CPO powers. However, using an undertaking to secure commitment from the owner to carry out works matched by a commitment from the authority not to use CPO powers if those works are done should allow the CPO process to be either aborted or uncontested.