^ the difference is, you're not living in AUS, affecting their economy on a daily basis and not paying into the tax system to level out your daily activity.

it's one thing to live in canada and do business with UK customers, you're fine on that because you live in canada and pay into the canadian system. to reside in the uk, you will have to pay into the uk system, which means either getting a green card, or whatever their equivalent to that is, being sponsored for citizenship, or looking into some kind of work vacation visa - apparently under this you can travel abroad and be eligible to work for short (eg 1 year) periods of time without having to invest yourself deep into the system, like a greencard of citizenship.

i'm all heresy, so if you're seriously interested in making the move, consult a lawyer - if you go in with at least some idea of what you want to do i imagine you can work out a reasonable retainer to get the answers you need - but generally, no you can't just fly over there and start charging money and not pay it back into the system you will be using (roads, healthcare, transport, etc).