Oh so it is my problem that you cannot figure out how to access the article. Okay here is another option for you:
http://classic.austlii.edu.au/au/journals/PrecedentAULA/2016/81.html
That is a rather lengthy article, and because I am not sure of how good your attention span is, I have cut and past the relevant passage and highlighted the key bit for you, just to make it easy for you.
‘NOT JUST A BUSINESS’: THE DEBATE AROUND CONTINGENCY FEES
By Michael Wheelahan QC
On 7 March 2002, the Hon Justice Michael Kirby addressed a function for the presentation of the Australian Law Awards in Sydney. Justice Kirby spoke of a time when the Australian legal profession was not so profit-oriented, of the days of highly personal involvement with a wide mix of clients of modest means, and of the days when the words
pro bono were unknown, because fee waiver was such a common fact of life. In his concluding words, Justice Kirby stated:
[1]
[2] The Working Group advocated the introduction of percentage-based contingency fee arrangements as ‘an additional option’ for clients to fund access to legal services.
In April 2016, the Law Council decided not to accept these recommendations.
The purpose of this article is not to weigh the pros and cons of contingency fee arrangements. Much that might be said to support such arrangements has been set out in the Law Council of Australia Working Group’s final report, and in other papers, such as a position paper prepared by the Law Institute of Victoria, which was released on 17 February 2016.
[3] The purpose of this article is to set out four reasons why percentage-based contingency fee arrangements are unnecessary, and undesirable, and why the Law Council was correct to reject their introduction.
The four principal objections to percentage-based contingency fee arrangements are:
(a) there is no apparent need for any alternative basis to charge fees to clients;
(b) a contingency fee arrangement treats a piece of litigation as a transaction, with no necessary relationship to the amount of professional time or effort required to prosecute the client’s case;
(c) contingency fee arrangements are inconsistent with the obligations of lawyers, and counsel in particular, to be independent of the client, and of the client’s cause; and
(d) the introduction of contingency fees will provide further opportunities for unscrupulous lawyers to charge amounts which are not proper, fair, reasonable or consistent with the standards of professional behaviour to which lawyers should aspire.
So you can take from that that contingency fees have never been allowed in Australia, that there was some push for their introduction from around 2013/4 and the Law Council of Australia confirmed that they would not be allowed, leaving the status quo in place.
Also, it is actually legislated in NSW:
LEGAL PROFESSION UNIFORM LAW (NSW) - SECT 183
Contingency fees are prohibited
183 Contingency fees are prohibited
(1) A law practice must not enter into a costs agreement under which the amount payable to the law practice, or any part of that amount, is calculated by reference to the amount of any award or settlement or the value of any property that may be recovered in any proceedings to which the agreement relates.
Civil penalty: 100 penalty units.
(2) Subsection (1) does not apply to the extent that the costs agreement adopts an applicable fixed costs legislative provision.
(3) A contravention of subsection (1) by a law practice is capable of constituting unsatisfactory professional conduct or professional misconduct on the part of any principal of the law practice or any legal practitioner associate or foreign
lawyer associate involved in the contravention.
