ML, it does, and has, happened in the UK, but not all that often, and the person doing it is usually regarded with a significant amount of opprobrium - and not only from their own party. It's (almost, I think) unheard of that someone who crossed the floor would be given a ministerial position, as happened in the last couple of Canadian administrations. Maybe after they'd served a year or so on the back benches, and even better if they've proved that they can win election as a member of their new party - usually they can't, unless they get parachuted into a nice safe seat, and even then they get punished by the electorate.
Floor-crossing is most common with an unpopular government and heading into an election, particularly where that government has a narrow majority. In these cases, it's MPs
leaving the governing party and joining an opposition party. Potential switchers will be courted assiduously - in secret, of course - by the opposition leaders, and then trumpeted as loudly as possible as a sign of how unpopular the government is. And then everyone in the switcher's new party avoids him/her, treating him/her like a plague-carrier...
In the
1992-1997 Parliament , where John Major's majority hung by a thread at times, there were a couple of big-name floor-crossers, notably Emma Nicholson and Alan Howarth. Unusually, Howarth was re-elected to Parliament in Blair's first landslide in 1997 - as a result of being parachuted into a safe seat - and was then made a minister. Emma Nicholson was not re-elected.
The most famous - and successful - floor-crosser ever in British politics was Winston Churchill. He was originally elected as a Conservative MP, but crossed the floor to the Liberal Party - still, in those days, numerous enough to form governments - and held quite senior ministerial office. As a Liberal cabinet minister, e was responsible for the first version of the minimum wage in the UK (arguing that without wage regulation the good employers are undercut by the bad and the bad undercut by the worst) and also set up the Labour Exchanges to help unemployed people find work. He later recrossed the floor to rejoin the Conservatives, commenting that
"anyone can rat, but it takes a certain ingenuity to re-rat.". His was without doubt the most successful political career there has been post-re-ratting.
Wendy
