Blair was the most successful Labour leader in history, electorally, no contest. Labour got over 400 seats twice in a row and had big majorities three times in a row. They lost when the opposition got its act together, Labour crumbled on its internal divisions, the economy slumped and genrally thre was a whole lot of bad luck for Labour. To wank Labour the New Labour approach needs to be sustained and the opposition needs to remain ineffectual and divided.
To do it best you;d need to rip the Tories apart. they came pretty close to that with the formation of the
Pro-Euro Conservative Party. Let's say that Clark and Heseltine and other important Europhiles, seeing no future in Hague's Tory party, join the Pro-Euro Conservative Party in 1999, and in 2000 it forms an alliance with the LibDems and they run several fusion tickets and use tactical voting.
2001 election sees Labour get about 430 seats, a majority of over 200 seats. The Tories collapse even further, getting about 120 seats while the LibDems get about 70 seats and the Pro-Euro Conservative Party gets a few more than 10.
The LibDems become much stronger, and Kennedy decides to target the Tories in 2005 in the hope of destroying them, avoiding catering to the left in the hopes of winning over Tory voters. A hollowed-out Tory caucus may keep IDS narrowly and becomes more and more divided. In 2005 Labour gets a majority of over 100 seats, losing many seats due to Iraq but still getting a huge win. The LibDems and the Tories are both clustered around 25%, and the LibDems get about 80-ish seats while the Tories return to around 150-160 seats.
Blair has a renewed mandate and is able to dispel challenges to his authority. The Tories opt for change but due to butterflies get David Davis instead of Cameron. Kennedy stays LibDen leader. Blair stays on until 2009, when he resigns and Brown takes the helm. Brown calls a snap election and voters opt for 'economic whiz' Brown. Labour gets 38% of the vote, the Tories get 29% and the LibDems get 23%. The seat count is 65-ish for the LibDems, less than 200 but more than 180 for the Tories and about 370 seats for Labour.
Brown manages to lead Britain through the recession, and begins to implement more timid deficit reduction measures. Labour heads into 2014 still relatively popular, and Davis is still Tory leader. Many voters do want change though and don't particularly like Brown. the election is held before the Scottish referendum. 2014 is close but the New labour formula comes out triumphant once more, with Labour winning by the skin of its teeth with 36.5% of the vote against 33.5% for the Tories. Labour forms a coalition with the LibDems and Gordon Brown retired in 2015, making David Miliband the PM.
Polls show the Tories with a slight lead now but there is no sign of a 1997-landslide. Tony Blair, despite his flaws, did one big thing. He made Labour the party of government.