interesting question there
The Conservative party at the time was stagnant, they no longer stood for anything other than clinging on to power* and we needed change, at the time I voted based on Blairs proven ability to cast off the worst of the historic Labour party dogma and lead us towards an economically successful** centrist vision of the future.
At the time I thought he had been more successful than he actually was in killing off the left wing loons, and as we saw it was only a matter of time before Gordon not only abandoned prudence, but subsequently beat her to death with a shovel and ran away claiming it was nothing to do with him***.
You could possibly argue that I’m naturally inclined towards transformative politicians as being the most effective in improving things (theory of constant revolution?).
* See also Labour after about 2006
**e.g.. ‘I will not allow house prices to get out of control and put at risk the sustainability of the recovery.’
*** See quotes from ‘Blair – A Journey’ and Lord Turnbull interviews here