I would definitely get your Australian citizenship, otherwise if you want to return in the future, you may have a problem. Having a British and Australian passport makes everything much easier.
You can get your National Insurance Number from Works & Pensions Department in Wales, they are helpful if you ring. Don't rely on the state pension here (when you need to) it is low compared to Australia.
London is a great place to visit and work. Living there is very expensive, so you would need a good salary. I am heading back to Australia this year after a short return to the UK, as realise I am more Australian than British now, even though I was born in London. However, its all different for me now and I am just glad that I have the option to return "home". Good Luck with everything.