http://www.expatistan.com/cost-of-living/comparison/london/sydney
about 1% difference compared with London according to that website....
From that website :
1.) Food in Sydney (Australia) is 24% more expensive than in London (United Kingdom)
2.) Housing in Sydney (Australia) is 2% cheaper than in London (United Kingdom)
3.) Clothes in Sydney (Australia) is 33% more expensive than in London (United Kingdom)
4.) Transportation in Sydney (Australia) is 21% cheaper than in London (United Kingdom)
5.) Personal Care in Sydney (Australia) is 62% more expensive than in London (United Kingdom)
6.) Entertainment in Sydney (Australia) is 15% more expensive than in London (United Kingdom)
Doesn't really compute to me - but I suppose they are basing the difference on the amount some people would spend on transportation. For most in Sydney - this would be virtually nothing.
As well as that - the website doesn't take into account the real things people need to spend money on. Childrens schooling, medical bills, Insurance bills and most importantly Beer (in a bar) - which is extortionate prices. The other point to note is that Sydney is also considerably cheaper than most cities for almost everything apart from the housing - but for 90% of people including myslef who have been to Australia & lived/worked in Australia - the cost of living is miles higher than the UK - and that's even when earning $100,000 a year.
As an example....
http://www.coles.com.au/portals/0/content/images/catalogue/current/c-nsw-met/Coles-c-nsw-met.pdf
Try getting a beer in Perth and your eyes would water.
Edit : Just checked and average price in Perth is $10 (£6.49) a pint, London is £3.50 ($5.39) - Funnily enough Sydney is also $5.39.