I believe Blair's father was a Conservative, perhaps if that friend at Oxford didn't push him left the young Tony would have been on the Clarke wing of the Tories. Of course, even if Blair didn't meet that friend he could very well have gone left later or at a similar time, usually people who shift politically are already heading in that direction once they meet someone or experience something that ultimately solidifies their political conversion.
That said, as a young Conservative Blair probably wouldn't have challenged Thatcher and he would have sat out the failed Tory coup against Major. Labour still wins in 1997, but after that the butterflies really start to kick in. Blair could either run for Conservative leader that year or support Clarke. If he runs, he wouldn't be strong enough to win in a crowed race unless he emerges as some sort of compromise candidate. On the other hand, Clarke came very close to becoming Conservative leader that year and with the support of the powerful Blair he could very well win. The Tories still lose in 2001 with Clarke as leader, but by a much smaller margin. And if the popular Clarke hangs on for 2005, the momentum from 2001 might carry the Tories to a stronger showing than Labour (In OTL the Tories were only three points behind Labour with the incompetent Howard). However, I don't think they'd be strong enough to win outright and the Parliament would be hung just like in OTL 2010. At that point Clarke forms a coalition with the Lib Dems. Blair would be at some important post like Chancellor of the Exchequer. If Clarke's government is successful, Blair might very well become his designated successor and win once Clarke steps down. However the timing would have to be perfect for all of this to happen and any number of unforeseen events could completely Blair from the roster of UK Prime Ministers. However, Blair had the ambition and charisma to be PM, so there's a likelihood of it happening at some point no matter what party he joins.