David Cameron has said reforms to the act of succession have been approved - paving the way for the first time in centuries for a first-born girl to ascend to the throne ahead of her brother.
The Prime Minister, in Australia for a meeting of Commonwealth leaders, had put the reforms at the top of his agenda for the summit.
The visit was cut short by the Eurozone crisis as he scrapped meetings in Japan and New Zealand to attend the talks in Brussels .
He maintained that the existing principle of male primogeniture is outdated, and has received a positive response from other Commonwealth countries to whom he wrote several weeks ago outlining his concerns.
Speaking as he arrived at the Commonwealth Heads of Government Meeting (CHOGM), he described the change as a "simple act of modernisation and one that's right for our time".
The Prime Minister continued: "The idea that a younger son should become monarch instead of an elder daughter simply because he is a man just isn't acceptable any more.
"Nor does it make any sense that a potential monarch can marry someone of any faith other than Catholic.
"The thinking behind these rules is wrong. That's why people have been talking about changing them for some time.
"We need to get on and do it."
The changes are designed to come into force for any future Royal children.
Observers of the monarchy say the wedding of the Duke and Duchess of Cambridge added impetus to the debate, reinforcing the need for change before any further Royal heir is born.
The apparent consensus among the 16 countries who count the Queen as their monarch will make a welcome change for the Prime Minister from the wrangling he observed at the meetings of European leaders in Brussels.
However, the meeting may not be entirely free from arguments.
A report compiled by a body of senior advisers to the Commonwealth suggests that the organisation has been too slow to deal with human rights abuses in the past.
Some countries are resisting moves to beef up the ability of the Secretary General to intervene in a more outspoken way in international controversies.