This is a bit earlier than your cutoff date, but consider: Thatcher doesn't withdraw from the 1990 leadership contest and loses to Michael Heseltine. The right of the party is outraged but is temporarily mollified when the Tories' poll ratings start to rise thanks to the removal of Thatcher. Heseltine wins the 1992 election with a slightly larger majority than IOTL.
The party still falls apart over Europe as IOTL, but due to Heseltine's stronger Europhilia and the perception that he knifed Thatcher the right is even more rebellious. Heseltine resigns around 1994-95 due to health problems and is replaced by John Major, who proves less-than-capable of managing the split in the party. Several right-wing MPs defect to UKIP, which is now being bankrolled by James Goldsmith (who doesn't launch the Referendum Party ITTL)
By 1997, the Tories are polling below 30% thanks to Tony Blair's immense popularity, the splits over Europe, various scandals, and the rise of UKIP. Finally, Major's affair with Edwina Currie comes out just before the election, which turns off even more Tory voters. The Conservative Party collapses to around 110-130 seats, its lowest total in history, while Labour and the Lib Dems eat into their heartlands. UKIP puts in a respectable performance and a few of the Tory defectors keep their seats.
William Hague becomes Tory leader and tries to move the party towards the centre, which fails to convince voters who've moved to Labour or the Lib Dems while turning off even more traditional Tory voters, who either switch to UKIP or refuse to come out and vote. In the end, in 2001 the Tories collapse in the popular vote, effectively tying with the Lib Dems, while UKIP get over 10% of the vote. The Tories fall to 100 seats, while the Lib Dems close in on then with 80.
The Tories, hoping to attract UKIP voters, elect Iain Duncan Smith as their leader, who proves to be just as disastrous as IOTL. The few remaining pro-European Tories start looking wistfully in the direction of the Lib Dems. IDS manages to stick around until the election, by which point the Lib Dems have solidified their position as the anti-Labour vote, putting together a rather fractious and contradictory coalition of centre-leaning Tories and Labour voters upset with Iraq and Blair in general which can only last as long as the Lib Dems don't go into government. In 2005, the Lib Dems become the official opposition, overtaking the Tories who fall under 20%. Labour's majority is reduced but remains in the triple digits.
Britain has become a dominant-party state, with Labour retaining huge majorities thanks to vote splitting and FPTP, the Tories being seen as redundant and losing ever more ground to UKIP, and the Lib Dems becoming the default opposition party but not really credible or entrenched enough to form government.
I'm sure this is implausible in some way, but it's the best scenario I could think of.