None of us can predict the potential fallout from Brexit, good and bad. What began as a vote of confidence in our institutions has shown them to be dangerously fallible. A country where people usually rub along together is now marked by a cultural and emotional rift.

If Brexit does continue to dominate our politics for years, will it mean a reform of our institutions, or a battening down of the hatches by a beleaguered elite? Will the House of Lords, having alienated its natural defenders, at last be seriously reformed? Shall we try to restrain the dangerously capricious powers of prime ministers? Shall we empower local government? Both Brexiteers and Remainers will be in a rather militant mood.

Outside constitutional matters, I can see two areas in which Brexit should be in the best sense challenging. The first is our policy towards the outside world. The second is education, in all its forms and at all ages.

Brexit was meant to usher in a new age of ‘global Britain’ — an idea one would think hard to criticise, though significantly it is much mocked by Remainers. As we have been diverging economically from the EU for two decades, a broader and looser set of relationships is surely logical. Why then the mockery? Because a persistent theme of our 20th-century culture has been ‘national decline’: military, economic, political, cultural. Readers will, I hope, forgive me for mentioning this again, as it lies behind much of our present turmoil. For ‘declinists’, Britain cannot exist outside a larger entity, however unsuccessful or unrewarding. Theresa May’s withdrawal agreement was an extreme expression of this view.

We might take a lesson from across the Channel. General de Gaulle decided that France must assert itself as an independent actor, even if that meant annoying his allies. Ever since the 1960s, France has followed a consistent national strategy. To create a European confederation with France at its head. To carve out a commercial and political role in the Middle East. To maintain a post-colonial presence in Africa and the Pacific. To foster soft power through La Francophonie, its copycat version of the Commonwealth. It is willing to use money, trade, aid, arms supply and troops in substantial numbers where necessary. Some of these policies may be failing or unethical —some certainly are. But they are based on a clear and consistent idea of France’s unique interests and obligations, to which politicians and officials are committed.

Do we have anything comparable? If we do, I don’t know what it is. Perhaps being best friends to the Americans (not always reciprocated), or loyal partners ‘at the heart of Europe’ (now exploded). But these are not a strategy: they are — or were — a substitute for a strategy, relying on others to define the aims. Yet if we choose, we are Europe’s leading state: one of the biggest economies, with the most capable armed forces, and with unique reserves of ‘soft power’. We are building two hugely expensive aircraft carriers, with several times the effective power of the German air force. What are they for? In which parts of the world are they expected to operate? Are these the same areas in which we make our main diplomatic efforts and give our foreign aid? If not, why not?

Our huge foreign aid budget is scattered to the four winds. It follows no plan. It is not concentrated in countries where we have close historic or political ties or where our aid can have a transformative effect. We do not even use it to give university scholarships to future leaders — once an invaluable and wholly benign source of influence. It is deliberately not aimed to further our interests. We rarely even insist (unlike other donors) that it should be acknowledged as ‘a gift of the British people’. Much of it is simply cash handed over to governments (for example, that of Pakistan) or NGOs. British officials exercise little or no effective control over its use or its effectiveness.

Yet Her Majesty’s government is not a charity: this is taxpayers’ money. Why should it not be used to further our legitimate interests, which include fostering good government, democracy and mutual trade? Should it not be as clear for Britain, as it is for France, what we aim to do in the world, why, and where? We should think seriously about whether we want to be more like France, or more like Sweden. But who will do the thinking? Brexit means someone must.

The other area that needs to be galvanised by Brexit is education, the key to our biggest social and economic problems. The free movement of people has brought some obvious benefits. Many who have come are young, hardworking and over-educated for the jobs they take — like the young Spanish graduate (a victim of eurozone austerity) who used to clean my office. This huge influx of labour since the 1990s has facilitated our low-wage, low-productivity economy.

It has meant that many poor people in depressed areas have been made surplus to requirements, existing on precarious, part-time, low-skilled work or on permanent benefits. Twelve months ago there were 1.4 million unemployed (people seeking and available to work), and another 8.7 million economically inactive aged 16-64 (not working and not seeking or available to work). Moreover, 790,000 under 25s were Not in Education, Employment or Training (NEET), 11 per cent of all people in this age group — a truly shocking statistic.

Until now there has been little pressure from business (happy to import cheap labour) to improve our often mediocre education system, whether in schools, in vocational training, in tertiary and higher education or in continuing adult education. It has been all too easy to disguise and ignore failures or just mediocrity. Of more than 3,000 state secondary schools, for example, only a small minority ever send candidates to Oxbridge, whose admissions tutors are desperate for more. The CBI considers that UK school leavers lack basic literacy, numeracy and communication skills, have poor self-management and are ‘underequipped for life’. Its solution? Not to demand better education and training, not to press for high-quality apprenticeships in every sector — but to demand more Eastern Europeans.

So schools can stick with outdated (so-called ‘child centred’) teaching methods that exhaust teachers and fail working-class pupils. Teachers leave the profession (or at least the state sector) in droves and more children are excluded for misbehaviour. A small number of state schools — at most a few dozen throughout the country, alas — are trying something radically different. I recently visited one: the Michaela Community School in Wembley, an inner-city school with more than a third on free school meals, a quarter with ‘special needs’, around half with English as their second language and with relatively large class sizes.

I realised something was different when I asked the man at the tube station ticket barrier if he knew where the school was. ‘Yes, my son goes there,’ he said. ‘It’s the best school in Britain.’ An unwavering application of simple principles is having remarkable results: high expectations, no excuses, consistent discipline, concentration on learning, teachers who teach and a serious academic curriculum.

The school disproves the patronising and damaging prejudice that children from poor and diverse backgrounds cannot learn difficult subjects and are bound to be bored and inattentive. I was amazed to visit a history class of 15-year-olds (almost entirely drawn from ethnic minorities) who could switch spontaneously from tactics at the battle of the Somme to the origins of English democracy, feudalism, and the Anglo-Saxon Witan. Not many Cambridge seminars could do the same. And these children are visibly happy, interested, confident and articulate — just what you expect at Eton or Winchester.

Why don’t all schools adopt these methods? Because there is a stifling weight of orthodoxy and ideology that is hard to shift. A realisation that after Brexit we shall need all our children to be properly educated and trained should help to shift it. Immigration has recently fallen. At the last count, 350,000 extra jobs were created over 12 months, while the number of foreign-born people in the labour force fell by 142,000 as the lower value of sterling and Brexit made Britain less attractive. Consequently, the number of UK-born people in work grew by 492,000. Moreover, wages are rising. Brexit should mean that every person becomes potentially more valuable, and more worth investing in. Business, local government and central government will need to cooperate seriously in educating, training and retraining the current and future workforce.

Education is not just about churning out a labour force, but enriching lives. In how many inner-city schools would you see chalked on a blackboard, as I did at Michaela: ‘An unexamined life is not worth living’? Children there learn that this country, its literature and its history are their possession, their inheritance, wherever they or their parents come from. They streamed into lunch all reciting a poem, yelling its final lines at the tops of their voices: ‘I am the master of my fate / I am the captain of my soul.’ I believed them! Not a bad motto for post-Brexit Britain, either.