With a decent to strong result, I'm quite confident that you'll be able to enter the University of Melbourne or indeed most other Australian schools (barring any silly problems like academic issues, because academics are really the only sort of serious requirement they have, and even then it isn't always very high for some courses - for Law and Psychology they should only be "above average" but for certain social sciences such as Economics, Econometrics, Statistics, or Actuarial Science they will be greater). Australian schools are actually very international-friendly, so MUFY (being Monash's program) would get you in easily.

Perhaps you haven't yet commenced the necessary checks, because the University of British Columbia only offers a JD, an LLM, and a PhD in Law. It's good to consider graduate destinations early, of course, but this is not relevant to your real (immediate) intentions.

Law in the UK is indeed quite competitive, but this really only matters if you're aiming for top dogs like Oxbridge, LSE, UCL, King's, and Warwick (for the standard A Level or IB student, the only real challenge is Oxbridge).

I cannot objectively comment on MUFY's competitivity or standards or how it compares to the A Levels, except that I study at a school which claims to be "one of the top universities in the world", and here we have students who come from everywhere and who've done one of A Levels, IB, UEC, SAM, MUFY, SATs and a plethora of other qualifications.

Of course, MUFY isn't the most universal qualification there is, but there is no question that you can get admitted to a school for Law in the UK - it's just that it may be harder if you're going for something in Britain's top 5. Economics at said schools is also highly competitive (note Oxford does not have straight Economics). Business, Accounting, Finance, Management etc are fairly easy to get into (again, Oxbridge will be the only real challenge for any course they have, unless you're doing Medicine which is competitive all over the place).

Not all Australian schools have Law at undergraduate level... while there exists an abundance of options in the UK.

ANU is reputable but its strength lies in the Arts, Humanities and some Social Sciences (Languages, Linguistics, Philosophy, Politics, Geography, International Studies, History, Sociology, Law), some of which LSE also excels at.

Melbourne would be stronger in Commerce/Economics/Statistics (LSE would beat Melbourne in these) although ANU is not far behind. If you really wanted to go to LSE and there were no special circumstances that would make you choose Australia instead, you should go to LSE.