Pretty much all they have to do is wait until the Queen dies and the position of monarch is vacant. The House of Commons has the ultimate authority to declare who is the new monarch, and rather than decide on who is the new King, they'd just leave the office vacant forever and pass some sort of British version of the "No Titles of Nobility Amendment" that the United States tried to pass (and ultimately failed to pass, but it became a non-issue here because we didn't invent any 'titles of nobility' to grant) that would prevent the government from making ANYONE ELSE into a Duke, Lord, Earl, Prince, etc., etc. I suppose the existing dukes, lords, earls, princes, etc. would be able to keep their titles for life (it would be considered tacky and demeaning to strip Prince Charles of his lifelong "Prince" status), but it would have no power, and as they died off, eventually there would no one left holding "british honours". Thus it would be quietly phased out over the decades.
Then they'd just have to pass some minor technicality changing the country's political identity as the "Commonwealth of Great Britian and Northern Ireland" (remember, the monarchy would be vacant, so this new law wouldn't conflict with the previous rule that all government institutions are bound to obey the crown) and that Parliment has the ultimate authority, with the Prime Minister being the final arbitrator on whether a bill becomes law, rather than "royal assent". They already created a "Supreme Court of the UK" in 2010, I have no idea what it does, but they could copy the United States version and give them the ability to determine the constitutionality of laws passed by Parliament, and just copy their offspring the USA further by remaking the House of Lords as a U.S. style upper house (they can copy Australia if that's easier). Again, basically like the Oliver Cromwell era, minus an Oliver Cromwell type figure running things.
“...The House of Commons has the ultimate authority to declare who is the new monarch...”
I didn’t know that. Thank you!
I think they like their monarchy, though. Traditions, culture, heritage.
But either way, they won’t have to worry about it. The muzzies will take care of that when they overrun the country, after out-producing the Brits with little brown babies, all named MoeHamHead.