Pick two suburbs with high proportion of apartments. Potts Point (and I expect now Green Sq/Zetland and Haymarket) have the highest density.
Only a few small parts of Sydney are considered dense (>8000ppl/sqkm) - 21 square km versus London at 330 for example.
https://blogs.crikey.com.au/theurbanist/2015/01/13/population-density-is-sydney-an-outlier/
Firstly a couple of minor points - the maps shown in the Crikey article date back to the 2011 census. Since then Randwick LGA has approved (and mostly been built) over 13,000 new dwellings taking the number from around 65,000 to just below 80,000. At the 2011 census figures of approx 2.7 people per dwelling - you can see how much of an increase this is.
I quoted those two suburbs as the State Govt is proposing to more than triple the heights for tower blocks of units (with no on-site car parking to boot) despite the CSELR cutting public transport (and other road transport) capacity by around 10,000 passengers/hour into the city in the am peak hour.
The Greater Sydney Commission has officially stated that as the CSELR is INCREASING public transport capacity then increasing density even more is fine. Trouble is just as Gladys was revealed in the NSW Auditor General's report to have mislead Parliament and the Community over the cost blowout being due to increased capacity - the contract signed actually REDUCED the capacity from the earlier claimed potential.
I and another person took the evidence (TfNSW public documents) to the AG and caused the investigation.
Back to the comparison with London - The public transport capacity of London (underground heavy rail et al) is many times that of Sydney. Have a look at the London Cross Rail project which will have around 34 to 36 trains an hour operating and built platforms two cars longer than currently needed to allow for future capacity increases.
With suitable public transport, school capacity, hospital capacity, public open spaces etc etc increased density can be handled.
That is not what we have in Sydney.
Take a tube ride around London's suburbs and outer suburbs and you will see public park/playing fields constantly. The opposite is the case in Sydney. Schools from Sydney Harbour through to Botany Bay have been at or over capacity since before 2010, many have now banned children running in the playground due to the risk of knocking down other children. They have also banned soccer and rugby balls for similar risks.
Finally - according to the study in the news over the last few days - it appears that Randwick LGA did not add one 'affordable' dwelling despite the thousands of new high rise (up to 12 storey in some locations) tower blocks built supposedly for that very purpose. Or at least that is what the local Politicians (State and Council) used as the excuse for supporting them.
Nothing to do with the trail of donations from the property developers to all parties of course.