Ah, "facts". Blair achieved power because he managed to buy off the media, and as a result didn't get demonized anywhere near as much as previous Labour leaders - thats why something like the windfall tax, which would have been absolute communism if anyone else had done it, was greeted as common sense.
He then "professionalized" the party, bringing in (and Brown was as guilty of this) a host of bright young things with the intention that they'd reshape Labour in his image - this worked to a degree, with the party membership changing as many left wing people left. The policy programme was also really clever, with many Labour voters stopped voting Labour as a result (he lost 4 million votes between 1997 and 2005). The drop in membership and insistence on a professional approach nearly bankrupted the party, which almost resulted in him being the first PM ever interviewed under caution.
This project then ran into difficulties when Blair was forced out; the bright young things turned out not to be so bright - first they failed despite several opportunities in removing Brown, then they lost the 2010 leadership election, then - convinced of their own popularity - they changed the rules for the next leadership election so that people from outside the party could vote in leadership elections, which would prevent 2010 ever happening again. The rest you probably know.