Can you clarify why you would like to create three english-language sites with separate audiences (is it a localized service, for example)? Is there overlap between the three audiences (SEO is more important) or is the Australian site completely useless to UK users?
Can you confirm that all your content is in English?
[added later] I realize in re-reading the question that all the sites under consideration are in English. I'll leave my original answer in case it helps someone else.
You are much better off having local domain names if possible.
There are multitude of ways to indicate which country you're in, but the domain name is a clear and universally recognizable way to say to search engines where you are.
As noted in the comments, it's impossible to prove these kinds of statements. However this is a no-risk plan: if it doesn't make a difference you lose nothing, if it does, you win or lose big.
If you have the choice, do it. It's trivially easy to setup using .htaccess and makes managing the site much easier.
[original answer] I manage a large site in three languages. We set it up as /en, /es, etc. after the domain name and I sincerely regret it.
There are several issues, but the main problem we ran into is managing Page Rank flow and the home page.
If you have a site in three languages, the home page is in which?
Do you make it a combination of all three languages, or do you pick one?
Normally a good home page would have lots of links to different parts of the site, and a fair amount of relevant text.
In a multi-language environment, do you include all the links and text in all the languages? If not, your site will be less effective in SEO. If yes, it's a mess for users.
The question boils down to Page Rank flow. In a regular single-language site, you want the home page to get the juice from the other pages.
In a multi-language site, that is no longer clear. You want a Spanish user to end up on the Spanish homepage in as few clicks as possible. Automatic redirection can be penalized.
We wanted the French site to appear first in French search results, so that users don't have to click through a language selection page. Our experience is that it is necessary to optimize for each language independently.
Having multiple languages behind a single domain name made it much more complicated to say to Google: this is our French site, in French, this is our Spanish site in Spanish, etc. It's mainly a question of Google knowing what language each page is in. Which language specification do you include in the home page header?
Also, it's true that you are slightly penalized for deep folder hierarchies (that being a hallmark of old blackhat SEO).
By using separate domains, you can cleanly and easily optimize each site with good Page Rank flow. If you do use a single domain, the best option we found is just to sacrifice the home page and push the Page Rank to /fr, /es etc.