by younger male siblings.
Labour MP Keith Vaz wants a repeal of existing law "to remove any distinction between the sexes in determining the succession of the throne".
His efforts have won much support in Leicester, from where he is an MP, but authorities in London have indicated that such a change in law may be difficult to implement.
If William and Kate's first-born is a girl, she would not be first in line to become the monarch if they later went on to have a son.
Vaz, who is chairman of Home Affairs Select Committee, believes the current law privileging the son is outdated.
"The law was outdated in the 21st century, where people expect that discrimination of any kind should not exist and there should be equality regardless of race, gender or religion," he said.
"Some of the United Kingdom's most successful monarchs have been women, no-one less than our present Queen, Elizabeth II. If the current succession laws did not exist, Princess Anne would be fourth in line to the throne rather than 10th, while her daughter, Zara, would be sixth in line rather than 12th," he said.
In a poll conducted by Leicester Mercury, a leading regional daily, more than two-thirds of readers agreed with Vaz and said there should be a change in the law governing succession to the throne.
Vaz argued in the House of Commons this week that rules should be brought in giving female children equal status.
"With the marriage of Prince William and Katherine Middleton, we have a once-in-a-generation opportunity to change the law. Prince William looks like a very modern prince. If he has a daughter first, it is only right that she becomes queen," he said.
But Constitutional Affairs Minister Mark Harper suggested changes would have to be dealt with alongside other constitutional changes.
"It's not as straightforward a process as some who would wish it to move more quickly might think," he said.