The OP isn't suggesting he'd remain a Trot, or even a Bennite. Even if he were, Labour housed plenty of radical leftists at this time, I can't see him leaving. But I think what is being asked is whether he could be a bit more like a Kinnock or a John Smith. He'd be more left wing, but still moderate enough to be elected off of the back of his charisma and the utter collapse of the Tories in 1997.
IMHO the utter collapse of the Tories in 1997 was in part due to Mr Blair and New Labour being as right wing as they were.
I think John Major and Mr Blair (correctly) deduced that what most British people wanted was One Nation Conservatism or "Thatcherism with a human face." John Major was unable to deliver it which left the field open for Mr Blair's "Thatcherism with a Cheshire Cat smile."
If Mr Blair had been more like John Smith or Neil Kinnock there would not have been an "utter collapse" of the Conservatives. I it would have been "merely" a collapse (i.e. less severe than OTL) at worst, but I think it would have been a "normal" victory with the Labour Party gaining a working majority.
The Liberals are likely to have done better in 1997 because some people who voted Labour IOTL would vote Liberal had Mr Blair been more left wing. However, because of the first pas the post electoral system it's likely that the increase in Liberal votes would not have produced a corresponding increase in the number of MPs elected.