Queen Elizabeth (pictured last October on a visit to St John's Beaumont School in Old Windsor, Berkshire) is said to have reacted coolly to the proposed changes.
The UK coalition government has dropped plans to reform the monarchy which might have allowed a Catholic to become king or queen.
Proposals to reform succession to the throne, permitting Catholics and women to have equal rights, were raised by Gordon Brown last year. Talks had began with leaders of 15 Commonwealth countries whose approval would be require to change the law.
But on Thursday, Mark Harper, Tory minister for political and constitutional reform, told MPs in a written answer: 'There are no current plans to amend the laws on succession.'
Roman Catholics were banned from the throne by the Act of Settlement of 1701, which secured the Protestant future of the monarchy. It laid down that the King or Queen must swear to maintain the Church of England. It also said no one married to a Catholic could succeed.
Before the election, the Liberal Democrats backed reform on the grounds that the rules of succession discriminate against Roman Catholics and women.