Party official: The Prime Minister is going to a fee-paying school tomorrow.
Shephard: Of course, he went to a comprehensive school yesterday.
Party official: No Gillian, he went to a grant-maintained school...
Shephard: That's right, a comprehensive grant-maintained school - like most GM schools...
Party official: But GM schools aren't comprehensives, they're grammar schools...
The conversation, involving a party worker at the heart of the Tory campaign, reveals either a startling ignorance of government education policy - or wishful thinking.
Either way, it helps to dramatise the confusion and fudge on an issue - selection - which some Tory insiders believe did much to blunt the party's appeal on education. Instead of projecting itself as the party of choice and standards - clothes which Labour had spent years busily stealing - it came under attack as the party which wanted to turn back the clock to academic selection, and that meant not just grammar, but secondary modern schools.
According to one well-placed Tory, who believes a return to grammar schools would be a mistake, ignorance about this key aspect of education policy is common in the upper echelons of today's Conservative party: "It is a cardinal belief in the party that there should be a wide variety of schools - specialist, GM and so on. We all agree on that. But there are a lot of people who do not understand what a grammar school is - and some of them are in quite influential places. "
As the Tory faithful prepare to gather for their annual conference in Blackpool next week, many have already begun a post-mortem on the most crushing election defeat of modern times. Most agree that specific education policies probably had little effect on the vote; that the party was defeated on the "big issues" of Europe, its handling of the economy, and sleaze. But at least some senior Tories privately believe that divisions - particularly on selection - added to the perception that the party had lost direction and become out of touch with voters.
One left-wing Tory, however, believes that John Major's public support for a widespread return to selection - a grammar school in every town - had a seriously damaging effect. Demitri Coryton, chairman of the Conservative Education Association, said: "I think it lost huge numbers of votes among parents with children at school and had a very damaging effect on informed opinion in education"
One of the few Tories among the new intake of MPs, Theresa May, acknowledges that the party must work hard to re-establish good relations with teachers and to listen to their views.
"We are at a point where we do need to reconnect with all those involved [in education] and what they want to see changed for the future. We need to give rather more attention to the teaching profession than we have in the past. I think one of the issues is the amount of change we imposed on people. Many teachers did not like the fact that we that we did not just change things, but that we changed and changed again."
This view is shared by Stephen Dorrell, the man charged with updating the party's education policies and developing an effective voice of opposition to New Labour. Mr Dorrell already appears to be preparing the party for a switch back to the centre ground, conceding that in the run-up to the election the party had lost the initiative.
"I think if a party suffers such a big defeat as we have it is important for our party to listen. There is no point in saying that we got everything right. We clearly need to learn from our experience. I think it is true that Labour carried greater conviction in the public mind as a party committed to delivering excellence in public education."
Mr Dorrell is not yet ready to talk about any specific policy changes. The party is about to embark on a fundamental review of all its policies and will not reach firm conclusions until much nearer the next election.
Meanwhile, he is about to embark on a series of meetings with teachers, parents, school governors, local councillors, lecturers and students - part of a strategy of rapprochement with the main stakeholders in education: "We clearly are very keen to use the early period of this Parliament to rebuild bridges with the profession and other parts of the education system," he says.
His immediate priority is to draw up a strategy for fighting Labour, in the hope of landing some heavy blows during the passage of its forthcoming school standards Bill. On this he is clear. The Labour party has already, in his view, shown dangerous signs of over-central isation, being too prescriptive on homework and too willing to interfere in the detailed running of schools. He is opposed to the Department for Education and Employment and local authorities being given stronger powers over schools.
Such a view finds ready support among Conservative intellectuals. Sheila Lawlor, director of the right-wing think-tank Politeia, not a natural ally of the left-leaning shadow education spokesman, says: "Stephen Dorrell is very keen on bringing forward the great Conservative themes - freedom, choice, responsibility, standards, quality. They are the themes and the means to have them are through deregulation and decentralisation."
The Conservative peer and privatisation guru, Lord Skidelsky, shares this analysis, believing the answer is to push ahead with market solutions for schools.
"The Tories went some way down the road to free up schools. But we still have a centrally planned, quasi-Stalinist system, with a national curriculum, testing, monitoring, closing down schools and sending in task forces. Labour is making that worse. I think the market should be allowed to run the system much more," he says.
While decentralisation and deregulation seems certain to remain firmly on the Tory agenda, it is far from clear whether Mr Dorrell will sign up for radical market solutions for schools - vouchers, the holy grail of the Right's true believers, for example.
He has yet to make up his mind on the controversial issue of selection, which continues to divide the party. There are signs that he believes that it is perfectly possible for grammar schools to co-exist with comprehensive s. But even radicals like Lord Skidelsky believe that it would be impossible to go back to a selective system, given its inevitable associations with the unpopular 11-plus.
It remains to be seen whether the back-to-grammar-schools agenda will finally be dumped by party modernisers, or whether free market nostrums like nursery vouchers will disappear from the agenda. But even ardent anti-vouchers campaigners like Demitri Coryton believe the market should still have a role to play: "I am not saying the Tory party should abandon the idea of bringing in the private sector to bring choice for parents. But vouchers didn't work because they were incredibly bureaucratic, " he said.
Mr Dorrell is likely to continue to take an interest in market solutions to some of the problems facing state education. But he is also anxious to rebuild the party's reputation for public service. "One of the important areas for the Conservative party is its attitude not just to education authorities but to local government as a whole. There are important elections to be held next year and we clearly need to have a stance, not least in the education field. It is part of the rebuilding process on which we are engaged to ensure we have thought through our view about the role of local government, in all its various aspects, and its relationship with central government."
Whatever happens, the future of the party's fortunes will largely depend on its young leader William Hague, himself the product of a comprehensive school, and his plans to make the party more democratic and accountable to ordinary members. Ironically, the pathway to changing unpopular education policies is likely to have as much to do with changing the party's image and appeal as holding policy reviews. That means making the party popular with the sort of young upwardly mobile professionals, currently flocking to new Labour.
According to one insider: "Politics are changing and we have got to realign ourselves. That means doing away with ancient selection procedures,which make it difficult for young professiona ls, especially women, to get a Tory seat. The people who select candidates are not even in touch with grassroots Tories, never mind professional people. "
As the inquest gets under way in Blackpool next week, the need to modernise the party machinery is likely to be the dominant topic. The test for William Hague will be to persuade the party faithful to open their hearts to change, so that the policies which brought their historic defeat can change.