For those who are cooped up in a flat at the moment with a baby and no garden, worrying about getting the government’s 80% income replacement after losing your job, the lockdown must be almost intolerable. Then there is the rise in people needing food banks and in cases of domestic violence – both predictable results of lockdown. For those working at home with a secure income and a garden, it is much easier.

Governments, careless of the contrasts between rich and poor, always want us to believe “we are all in this together”. In the wake of the 2007-8 financial crisis we didn’t buy it: we remained strongly aware of divided interests and circumstances. However, this time, despite the stark differences in people’s experience, there is a strong feeling that we really are in it together. As with other great challenges, most notably the second world war, the present crisis has given rise to more neighbourliness, sociability and a desire to take care of each other.

It may not yet be more than skin deep, but our society has begun to change. Street by street, up and down the country, schemes have been set up that are creating more cohesive communities. WhatsApp groups, set up to identify and provide support for the vulnerable, have brought neighbours together to help each other out.

People seem to have become friendlier. Out exercising, they stop to talk as they rarely did before. Even class differences seem less of a barrier as we have become more aware of what really are, and are not, “essential jobs”. People obviously take pleasure in this newfound sociability – and it’s not just sentiment: the appeal for 250,000 voluntary helpers to support the NHS and the vulnerable was oversubscribed several times over.

Nor has the government remained immune from this spirit. To support people who have lost earnings, it suddenly assumed responsibility for paying the wages of a large part of the labour force. Elsewhere, policy has undergone a complete volte face. The 2025 target for ending homelessness suddenly became an instruction to local authorities to house rough sleepers “by the weekend”. And where previous governments have failed to tackle suicides and violent deaths in prisons, the government is planning to release 4,000 prisoners early to reduce the spread of Covid-19. Similarly, despite having ignored the growth in food bank use, the government now has a scheme to deliver food parcels to the vulnerable.

The point is not to suggest that the results of the pandemic are somehow balanced between good and bad. It is simply to recognise that, alongside the pain and damage, there has also been an increase in social cohesion, friendliness and mutual support. Although the gaps on supermarket shelves suggest there has been antisocial stockpiling, a study of 30,000 people’s purchases showed stockpiling was rare: only about 6% of people hoarded hand sanitiser and 3% dry pasta. The problem was mainly that most of us bought just a little more.

To people like ourselves, immersed in research on the effects of reduced income differences between rich and poor, the increase in sociability looks familiar. Numerous studies show that community life is stronger in more equal societies. People become more public spirited, they trust each other more, are less out for themselves and more aware of the common good. They are more likely to help each other out, including elderly people, disabled people and those with mental illness. And instead of just looking socially upwards to the highest paid and down on the lowest, smaller income differences make it easier to see the real value of what people do. It is as if greater equality changes human nature.

While some of what we have seen during the Covid-19 crisis seems to echo the social benefits enjoyed by more equal countries, greater equality is not the explanation: income differences in the UK are likely to have widened rather than narrowed during the crisis, as the low-paid lose sources of income while higher-earners who work at home continue to draw salaries. But other things can also make us feel we are all in it together.

Just as income inequalities and social class differences are divisive and give rise to opposed interests and perspectives, being in the same predicament creates unity and shared interests. Hence the pandemic has brought us together in the same way that research shows greater equality does. Both make us feel we have more in common.

Because greater equality is so enabling, it has been used to get people to pull together in difficult circumstances. In his 1958 essay on War and Social Policy, the pioneering researcher Richard Titmuss said that because “the cooperation of the masses was … essential [to the war effort], inequalities had to be reduced and the pyramid of social stratification … flattened”. Egalitarian policies were therefore implemented to make people feel the burden of war was fairly shared. Income differences were reduced by taxation, essentials were subsidised, luxuries taxed and food and clothing were rationed. Another quite different example comes from the explorer Ernest Shackleton. During his exploration of Antarctica he “loosened some traditional hierarchies to promote camaraderie”, and distributed “the ship’s chores equally among officers, scientists, and seamen”.

When we eventually emerge from the Covid-19 pandemic, governments will still be faced with the climate crisis – putting us on the same planet, if not in the same boat together. But here too, inequality is a problem. International agreements are stymied between high- and low-income countries – one with primary responsibility for carbon emissions and the other in greater need of development. Given that the environmental footprint of the rich is massively larger than that of the poor, inequality also matters within countries – see the gilets jaunes opposition to Emmanuel Macron’s fuel tax.

In our 2009 book The Spirit Level, we demonstrated that greater equality not only improves social relations and wellbeing while reducing health and social problems, it also helps countries do better environmentally – leading to lower carbon emissions per $1 of GNP, more recycling, and business leaders increasingly engaged with environmental issues.

Because the huge rise in inequality under Margaret Thatcher during the 1980s has not been reversed, Britain has become a more anti-social society. But for that, we would now be in better shape to face the Covid-19 pandemic and to transition to sustainability.

Forced by the pandemic, the government has at last put human wellbeing before economic growth, and the Covid-19 crisis has reminded us all that we can be a more sociable and caring society, that we enjoy it and it makes society stronger. If we are to maintain these benefits as we move from here to tackle the climate crisis, it is essential that governments commit to reducing differences in income and wealth.

• Richard Wilkinson is emeritus professor of social epidemiology at University of Nottingham and honorary visiting professor at University of York. Kate Pickett is professor of epidemiology at University of York. They are the co-authors of The Spirit Level and co-founders of The Equality Trust