Does the time difference between London and Sydney change during the year?

Yes. Because of daylight saving time the gap moves between −11h and −9h.

When is the best time to call Sydney from London?

There is no overlap between standard working days, so one side has to call early or late.

London is 9h behind Sydney. This gap is not fixed: daylight saving time moves it between −11h and −9h during the year.

London

United Kingdom

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Sydney

Australia

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A 9-to-5 working day in London does not overlap one in Sydney at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
London · United Kingdom	Europe/London	UTC+1
Sydney · Australia	Australia/Sydney	UTC+10

What is the time difference between London and Sydney?: London is 9h behind Sydney. This gap is not fixed: daylight saving time moves it between −11h and −9h during the year.
Does the time difference between London and Sydney change during the year?: Yes. Because of daylight saving time the gap moves between −11h and −9h.
When is the best time to call Sydney from London?: There is no overlap between standard working days, so one side has to call early or late.