What about having either Labour or the Conservatives (probably easier to do the latter) totally implode at some point in the time period, leaving, presumably, the Liberal Democrats to become the Official Opposition.
Let's be interesting here.
Blair takes power as OTL, and the Tories continue to shred themselves, badly. Makes the OTL period 1997-2003 look like a walk in the park. Meanwhile, the Lib Dems begin to prise Labour out of power by attacking them from the left, and eroding their strongholds. Blair-Brown Labour eventually becomes the Right-wing alternative to the socialist(ish) Lib Dems, and end up going into Coalition with the rump Conservative Party.
Of course, this requires the British people to break with the habit of a lifetime and stop voting for who their parents did, whether that be Labour, or Conservative. And, I suspect, it's achieving this change in electoral mentality that ultimately is what makes many scenarios involving the destruction of the two party system in British politics very implausible. Does anyone else agree?