Healey had to cut public spending in real terms and did so with brutal gusto. It was the end not just for Keynesian economics as applied by successive Labour and Conservative governments, but for tax-and-spend socialism too. After the conference uproar Healey became a demon figure for many Labour supporters and, though he managed extraordinarily well in a tough situation, his austerity helped bring about the trade unions' "winter of discontent" and thus the triumph of Margaret Thatcher.
Undreamed-of levels of unemployment followed. Inflation became public enemy number one, with trade unionism running it a close second. The Labour Party itself came very close to destruction. Today, its attitudes to inflation, tax, public spending and the unions are all heavily marked by the trauma which broke upon it once at Blackpool.
Yesterday Mr Brown thumped out the hard lesson yet again: "No quick fixes. No easy options. No magic wand solutions by cooking the books or juggling the figures . . . No retreat into one nation isolationism. No unsustainable dashes for growth. No wish list spending solutions . . ." It could serve as a shrewd sub-editor's precis of the speeches made by Healey and James Callaghan 20 years ago.
The intervening period has seen Labour struggling first to accept this message and then struggling to discover a new message of its own. The latter has proved more difficult. Yesterday, Brown told the conference he did not want Labour to stop dreaming dreams or to water down its idealism. And, certainly, proposals on youth unemployment, the minimum wage and lower taxes for the poor all address real Labour concerns, even if in untraditional ways.
But if Labour wins an election this year or next, Brown cannot be a traditional socialist. He has no choice but to be an iron Chancellor in the Healey mould, tough on inflation - at least as tough as John Major and tougher than Lord Lawson. He cannot allow public spending to grow much as a proportion of national output. He cannot greatly raise taxes for the better-off or business.
Within these strict boundaries, there are local things a Chancellor can do, and Brown makes a vivid rhetorical case for doing them. But it was striking that, of the next big choice to confront the managers of the British economy, he said barely anything. For after Healey, and the Thatcher years, the dilemma now is whether or not Britain formalises its adherence to the new orthodoxy by joining a single currency.
That is a great political question, splitting the Tory party in 1996 more drastically than the IMF crisis and its consequences split Labour after 1976. But it is not, apparently, big enough to merit serious discussion in public by the Labour leadership.
Let us hope that Tony Blair turns to it today. Because the other thing about that stormy Labour conference of two decades ago is that big truths were hurled around the floor; it was a moment of trauma for our politics, but also a time of honesty and openness. And that is another part of Healey's legacy that Labour should never forget.