While the Conservatives did their thing in Blackpool, the common rooms of Britain held their own conservative gathering in Dublin, where the Headmasters’ and Headmistresses’ Conference had its annual knees-up.

The HMC is the club for Britain’s most prestigious private schools. Three hundred were there, from Abingdon to Yarm, taking in the big guns like Eton and Harrow, although not Winchester - still blackballed since the sudden departure of former head Dr Nicholas Tate.

It was not a radical congregation. The uniform dark suits and spectacles made it look like a convention of freemasons, with few skirts and necklaces on show.

What, then, to make of the chairman’s address, delivered by Graham Able, master of Dulwich College in south London? He kicked off the proceedings with an attack on a cornerstone of government policy, namely assessment.

Tortuous comparisons of A-levels over time are “irrelevant”, he said.

Teachers need more trust and freedom. Schools need more sport, art and music. Independent-sector scholarships should be turned into bursaries for the poor, and private schools should eventually take pupils on ability alone.

On some sort of reckless roll, he described lawyers and accountants as “vastly over-rewarded”, although sensibly avoided mention of bankers. The Allied Irish Bank later staged a buffet of Roman grandiosity for the assembled heads.

Then came the killer blow. “We should not,” said Mr Able, “connive at the construction of so-called league tables.

“Despite the positive press they give to our sector in general, there is concern over the effect these tables have had in restricting A-level subject choice, and even debarring reasonable candidates from some sixth forms.”

The heads are still reeling from allegations of fee-fixing, of course, and the reported interest from the Office of Fair Trading. But on this the conference was silent.

Few in the audience believed that league table UDI is practical. Private schools, like their state counterparts, have to give their results to the Department for Education and Skills, and many do well out of the publicity.

There were doubts about other aspects of the speech, too. Some delegates, for example, were surprised to learn of the rising tide of social chaos threatening the private sector. Mr Able lambasted “selfish and self-indulgent” parents, who place their own relationships above the welfare of their children. Broken homes are now a significant factor, he suggested, placing an extra emotional burden on schools while some angry parents refuse to continue paying fees.

Public schools, as Mr Able suggested, have changed beyond recognition, even if the suits look familiar. And most of the heads agreed with most of their chairman’s speech. Here, in the comfort of an oversized hotel, was a view of education fantastically at odds with the regime laid down for state-sector colleagues. And, in comparison, positively liberal. Little wonder that the conference was held a long way from Whitehall and the OFT.