Not to go all arcane on you, Mona, but it’s not clear that Brits have the constitutional authority to change succession rules. According to the 1931 Statute of Westminster:
It would be in accord with the established constitutional position of all the members of the Commonwealth in relation to one another that any alteration in the law touching the Succession to the Throne or the Royal Style and Titles shall hereafter require the assent as well of the Parliaments of all the Dominions…
– ie, Canada, Australia, the Bahamas, Papua New Guinea, etc. Good luck getting that agreement.
On the other hand, that’s part of the preamble rather than the enabling acts, so there are constitutional scholars who argue each realm could amend its own succession according to its taste — male precedence, female precedence, gay-partner-of-the-younger-son-of-a-royal-duke precedence, Muslim-son-of-the-third-wife precedence. So a generation down the line you could have Emir Charles reigning in London, but Queen Autumn (the Canadian wife of Princess Anne’s son) reigning in Ottawa.
Incidentally, given the collapse of marriage as an institution in Britain, why are those born out of wedlock ineligible to succeed (the son and daughter of Viscount Lascelles)? If Gordon Brown wants to be a la mode, why doesn’t he get all his non-discriminatory ducks in one row?