The Succession to the Crown Bill will go through its first two parliamentary stages at Westminster today and then through the remaining two next Monday. The legislation will end the principle of male primogeniture, meaning men will no longer take precedence over women in the order of succession.
A consequence of this will be that the Duke and Duchess of Cambridge's first child will become monarch even if it is a girl, who later has younger brothers. The legislation will also end the bar on anyone in the line of succession marrying a Roman Catholic.
However, crucially, it will maintain the rule that the monarch has to be an Anglican, so that he or she can hold the role as Supreme Governor of the Church of England.
Yesterday, the Cabinet Office pointed out MPs had received a letter from the Church of England expressing strong support for the bill.
Ahead of the debate, Nick Clegg, the Deputy Prime Minister, who will lead for the UK Government, said: "The reforms couldn't be more timely, given the fantastic news that the Duke and Duchess of Cambridge are expecting a baby. The other Commonwealth countries where Her Majesty The Queen is head of state have just given us the green light to change the law and we are wasting no time."
He explained the Government was modernising "out-of-date rules so men and women in line to the throne have equal rights".
However, the Lords Constitution Committee said fast-track procedures would "rarely, if ever, be appropriate for significant constitutional matters".
Baroness Jay, its chairwoman, added: "Recent commentators have raised possible unintended consequences of the bill. The committee is of the opinion that those matters are the kind of issues that Parliament must have suitable time to discuss; that will not be the case if the legislation is fast-tracked."
In response, a Cabinet Office spokesman insisted two days of debate in the Commons was ample time for such a measure given it had cross-party support.
l A Perthshire mother who suffered the same acute morning sickness as the Duchess of Cambridge will take her campaign for better NHS support to the Scottish Parliament today.
Natalie Robb, 25, is calling for specialist nurses to be on hand in Scottish hospitals.