The oldest house on the street ...

Any guesses?  It is actually "Larkhall" at 53 Cambridge Street.  That is according to the Paddington Rate books.  These rate books were maintained by council and list each owner on each street and what the property is (i.e. land or house).  They contain a lot of information, usually including the resident, the assessed council value, the annual rates and the invoice number and date paid by the owner.  Given the books record financial transactions it is probably a little more reliable than the Sands Directory.  You can find them on microfiche at the Woollahra Local History centre.

Cambridge Street makes its first appearance in the rate books in 1885, following the subdivision of the Duxford estate.  Rates were paid on the value of the unimproved land.

The first two houses were built by 1886.  They were both owner occupied and include Thomas Lawler at 57 Cambridge Street and Robert Bruce at 53 Cambridge Street (although street numbers don't actually appear until the 1889 rate book, both gentlemen continued ownership through to then).  I am not sure which came first (and have speculated previously on this) but given 57 Cambridge is now the playground then 53 Cambridge wins by default.

The rate books are an interesting record to see how the street developed.  I had assumed it was built from the Gurner street end down but that is not the case.  On the east side the group of 5 terraces from 61 to 69 Cambridge Street appear to have been built by 1887 whilst its next door neighbour at 59 (Frampton) is dated 1889.  Similarly on the west side 36 to 40 Cambridge Street appear to be built by 1887, while 22 to 34 are not built until 1890.  Of the 4 houses at the end of Cambridge street (constructed by the same builder, the Allum brothers) it was 46 Cambridge that was built last (by 1890) whilst 48 to 52 Cambridge were there in 1889.