The obvious example of this is from May 1940. Churchill became Prime Minister because he could command the support of the Commons as the Labour Party were willing to enter a coalition with him as its head. Churchill was not the leader of his party, the Conservatives, as Chamberlain retained this role.
Small nitpick. Labour isn’t a minority party, unless you mean in the strict sense that they don’t (currently) hold the majority of seats in Parliament. They are the second largest party and the Official Opposition to the Government, which is an important element of our Parliamentary system.
If the Tories are our Republicans, then Labour are the Democrats. They are the party of Blair and Brown.
The problem with Corbyn’s leadership challenge is that, now more than ever, we need a strong opposition to challenge this shit storm the Tories have created and hold them to account on their decisions in the coming months and years. Instead, they are squabbling amongst themselves, which is no use to Labour and no use to the country.