The history of this is that he and Ashdown had more or less agreed the terms. There would have been two senior Libs in the cabinet and Labour would have agreed to Lib demands on PR. Ashdown would not have been in the cabinet, but would have remained LD leader.
At the time, people assumed there would be a minority Labour government. The Libs would have been necessary to make up the numbers. But Blair reportedly suggested that even with a fairly small majority, a coalition would have been viable to ensure a stable government (as in, backbenchers wouldn’t have been able to play their games). I don’t recall the exact figures there, but it was something in the region of a majority of a few dozen.
In the event, Labour’s majority was huge, but Blair was reportedly still considering a coalition because it would have upended British politics and dramatically reduced the chance of a future Tory win. (He also apparently suggested the two parties merge, but that was turned down.) What stopped a team-up is a couple of Labour heavyweights saying they would resign in protest. Blair put party over country — and again when kicking AV+ into the long grass — and thereby arguably missed two massive opportunities to overhaul UK politics. The second, arguably, was the bigger blunder, in my opinion, though.
Labour subsequently descended into hubris. It felt it deserved to rule — and rule alone. The nadir was the 2005 win, where the party secured 55% of the seats on 35% of the vote, massively at odds with its reformist stance elsewhere. Here was a party then no different from the Tories, wanting 100% of the power on barely more than a third of the votes. At that point, the shift to PR should have begun (not least when you had Kennedy’s Libs with 9% of the seats on 22% of the vote), but Blair by then had shifted. Today, he argues PR won’t fix anything.
It’s quite something that the one thing Blair, Corbin and Starmer all have in common these days is that they don’t want a representative parliament and fair votes. I suppose Labour folks should cheer that there is at least that one thing that unifies the party. But it’s also the one thing likely to perennially leave Labour the biggest loser, exiting elections and blaming Libs and Greens for not backing Labour, when a better alternative is for those parties to work together in England (while Plaid and Labour work together in Wales to oust the Tories there).