I am an Australian Citizen living in London on a holiday working visa. I want to live somewhere else in Europe for at least 12 months (probably France). Are there separate holiday working visas for each country in Europe/UK or does my current holiday visa cover all of EU/UK?
Each Working Holiday visa is an agreement between the country of your citizenship (Australia) and the country issuing the visa. Not all counties offer working holiday visas, and if they do, they don't offer them to every country either.
When I was of working holiday visa age, I found Anyworkanywhere to be handy - I've set it to show the working holiday visas available to Aussie citizens.
As you can see, there are a few in Europe that may interest you, but you'll have to apply for each one individually, and they do have different rules (some are up to 30, for example, while others are 35).
Yes, holiday working visas (and other long-stay visas or work permits) are separate for each country. Apart from a few general rules and very limited programs like the EU blue card (not fully implemented and not everybody participates…), the EU has no common policy regarding immigration from outside the union.
Whether holiday working visas are available to you as an Australian citizen also depends on the country: Those visas are based on reciprocal agreements and do not exist everywhere or for everybody.