Palmer's Index to the  Times:

http://news.google.com/archivesearch

Times, The
Monday, March 03, 1788 (London, Middlesex
Ensign Ensign Soot Sunpson srwm Soot h.isc Lest Kme-strcct parisli Hearsey Srancis parish sen Lankshear Oxsord Jesscry Oicsord-sti'eet Ilhtltiister Somerset ...

The Times (Newspaper) - January 11, 1831, London, Middlesex
Subscription - The Times - NewspaperArchive - Jan 11, 1831No extra Su Further paniculan be known on applirai on to Mr, H. lankshear. surjm.n. 3, f.itter ham-court, Mri, ounar. Crown ttrert, and Hr Seaint., SV.MI. ... 

      1 BANKRUPTCIES
      Lankshear, W. jun.
      Wednesday July 27, 1814
      Page 2, column c
1814 W Lankshear BANKRUPTCIES

      2 BANKRUPTCIES
      Lankshear, Joseph
      Saturday December 27, 1845
      Page 4, column a
1845 Lankshear, Joseph BANKRUPTCIES

      3 CRIMINAL TRIALS
      Lankshear, Robert, for Embezzlement
      Saturday December 10, 1870
      Page 11, column d

"Is this the Robert went to NZ in 1873?" 
1870  Lankshear, Robert, for Embezzlement

Source Comment from Kind Soul who did lookup

The index is on CD at large libraries both in UK and all over the world, I
manage to access it online though a university database which is why I do
lookups for people, it's so easy for me.  It costs a fortune to buy though.
To look at the films I usually go into London where they have a complete set
of all the years, once again your big library in Sydney should have them.