The trick with relocating to London, or anywhere in the UK, or anywhere in the world, for that matter, is qualifying for a visa to live and work there. It can be extremely difficult to get a working visa for the UK unless you have some special qualification, experience or training that is in short supply in the work force there. And, unless things have changed in the years since I was living in the UK, you still pretty much need to find a job first and then apply for a visa (or let your employer handle the paperwork). Long-distance job-hunting is tricky.

Australia, on the other hand, has a point system whereby you can qualify based on job skills and other criteria and then start looking for work once you get there. (Canada has a similar system.) OK, you need savings to tide you over until your job hunt pays off, but at least you're on site and available to take any and all interviews.

In any event, it would be a good idea to make at least one or two exploratory runs to any country you're considering immigrating to - just to check out general conditions, the job market, expenses, weather, housing, etc. etc. I'm constantly amazed by the number of folks who are planning to pack up and move the whole family half way around the world to a place they've never been to before.
Cheers,
Bev