An overhaul of the British constitution that would end the exclusion of Roman Catholics from the throne and make it possible for a first-born daughter to succeed ahead of any subsequent sons has been drawn up under radical Downing Street plans.

The reforms would also see the powers of the Privy Council curbed, in particular its role as judge in disputes between the UK Government and Scotland or Wales.

The proposals have been drawn up by Chris Bryant, the MP asked by Gordon Brown to review the constitution. The report has been handed to Wilf Stevenson, the Prime Minister’s adviser on the constitution.

Sources told The Guardian that Downing Street would like the new laws passed quickly in a fourth new Labour term. Mr Bryant is understood to have briefed a constitutional pressure group at the party conference in Manchester this week.

His report calls for an end to the requirement that the succession to the throne automatically pass to a male, meaning that if Prince William’s first child was a girl, she would become heir rather than any younger brother.

Ministers were also said to feel uncomfortable with it being illegal for a Catholic to become monarch in modern Britain.

The 1688 Bill of Rights, the Act of Settlement in 1701 and Act of Union in 1707 have all ensured that Catholics are barred from succession. On accession, the monarch is required by law to make a declaration before Parliament rejecting Catholicism.

Reformers argue that aspects of the Act of Settlement institutionalise religious discrimination and sexism. Many people have been blocked from taking a place in the order of succession because of the Act. Most recently, Prince Michael of Kent and the Earl of St Andrews were barred from their right of succession through marriage to Catholics.

Commonwealth nations would be required to approve any change before the proposals could become law.

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