Err Wilson/Callaghan,anyone?
Buy more importantly you're missing my point- by a mile. It was certainly true that whilst the neoliberal era was in full flow, you probably couldn't win it for Labour on any platform bar a Blairite one.
But then came the Crash, and a decade of austerity. One of the consequences of that has been to fully finish off the neoliberal era, another is the complete collapse of liberal centrist politics. .
All over Europe (and America), the voters have overwhelmingly rejected them. When Labour swung left in the 2017 GE,they reaped a simply huge increase in their vote.
Conclusion: keep tacking left, Labour, times have changed