This is what keeps being said, but it is very questionable how true it is. Take the actual legacy of "New Labour" for example:
i) 220,000 members
leaving whilst they were in Government
ii) 4 million votes
lost whilst they were in Government
iii) 161 seats lost whilst they were in Government
iv) Scotland transformed from a safe area into one where they have one seat.
1997 is the one genuine victory they can lay claim to, and that was by far and away the most left-wing manifesto that Blair ever ran on (windfall taxes on privatized utilities, a minimum wage etc). Far from Corbyn threatening the future of the party, it is the moderates getting back in control that presents an existential threat to their ongoing existence - they are already threatening to ignore some areas (the few remaining solid Labour areas) because they are
"anti-immigrant" and voted against the EU.