Peers voted by 74 to 53 to ask the Queen for permission to introduce a Bill which would make Princess Anne fourth in line to the throne.
Lord Archer pointed out that the measure would be unlikely to have any effect for at least 50 years. The Prince of Wales would still succeed to the throne and would be followed by Prince William. However, if Prince William's first child was a girl she would be first in line to succeed him.
Because of the Bill's nature, the Queen must be asked if she is happy for it to be debated. She is thought to be highly unlikely to reject it.
After the vote, Lord Archer confessed that he was slightly surprised that peers had demanded a division on the issue.
He said it was unlikely to find enough parliamentary time to become law before the general election, but he hoped it could be re-presented soon afterwards.
"I feel very strongly that as this isn't going to matter for 50 years it would be wise to get it out of the way," he said. "In 50 years' time our grandchildren will consider it farcical the first-born isn't automatically the monarch."
The last time such a motion was presented to the Lords, in 1994, there was no vote. The Bill, which would have let oldest children succeed to peerages regardless of their gender, was rejected at second reading.
Lord Archer's measure will meet some opposition, partly from hereditary peers who fear it will lead to a re-examination of their own position.
Among those who opposed yesterday's humble address were the former Lord Chancellor, Lord Hailsham, the former Commons Speaker, Lord Weatherill, and the Liberal Democrat, Earl Russell.
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