Yes, mostly they did. But New Labour was maybe more redistributive (eg NMW, tax credits) & didn't insult our intelligence. And its lack of challenge to capitalism was more forgivable as the economy wasn't in the grip of rentierism & stagnation.

The difference is that there isn't a figure like Gordon Brown in the current labour administration

When I read Blair's Doctrine of the International Community, I thought he sounded like a guy who'd underestimated the power of the money markets. Certainly NL get some credit for attempting all the Third Wave/NPM stuff in good faith. Now we're aware of its limits, it's less forgivable.