One the eve of the 2015 election, one that most pollsters thought David Cameron would not win, Boris Johnson gave perhaps the most interesting and insightful interview of his career. Sensing the ball was about to come loose from the back of the scrum, as Mr Johnson might put it, he told the Spectator magazine that the Conservatives were finished if they continued to be seen as defenders of the rich and, particularly, the privileged. He argued that “the wealth gap has been allowed to get too big” and is now “outrageous”. His post-mortem assumed that Mr Cameron was politically a dead man walking and about to be felled in a living standards election. Not for the first time, Mr Johnson’s timing failed him.

Mr Cameron won. Mr Johnson had to wait another four years before he got his chance to run the country. His instincts, however, were right. The Tories are seen as “for themselves”, “out of touch” and for rich families and pinstriped City workers. Voters don’t look at the Conservatives and see themselves. Yet Mr Johnson campaigned to become Tory leader on a platform of tax cuts for the rich combined with a staunch defence of bankers. He was bankrolled by billionaires and hedge fund managers. Mr Johnson’s outreach to the rich was understandable given that six out of seven of the voters he was canvassing do not believe that government should redistribute income from the better-off to those who are less well-off. That explains why Mr Johnson has backed the Laffer curve, a discredited theory that claims lower tax rates for the rich will lead to higher tax revenues.

Now Mr Johnson is in office. He has fired up the grassroots. His problem is that he will at some point soon have to go to the polls and fish for votes from leave-voting sections of society. Here it would seem he needs to convince people to vote against their economic interests. In the 2016 Brexit referendum it was the richest 30% who voted enthusiastically to remain in the EU. The bottom 70% preferred to leave. The frequently cited reason for this cleavage is that the poor and uneducated are nationalist and xenophobic. However, it is unlikely that the racism of the poor is any more natural than that of the rich. The French economist Thomas Piketty has a simpler explanation – that the EU was part of the dynamics that drove inequality on a global scale. Mr Piketty claims the EU was “based on competition between countries, on fiscal and social dumping in favour of the most mobile economic actors and functions objectively to the benefit of the most privileged”.

The idea that the EU is part of a project that has worked against the interests of the poor has been carefully cultivated on the extreme ends of the left and right. What neither side will admit is that domestic policy was not mobilised in the last few decades to ensure that international competition did not create too many losers. Mr Johnson will not assuage the anger felt in Britain by simply making people better off. Once inflation is taken into account, average earnings are £5 less per week today than in April 2008. His welcome plans to increase public spending will help reduce levels of private – and hopefully household – debt.

If Mr Johnson is serious he will have to deal with the UK’s damagingly high levels of inequality. The latest work suggests the gap between rich and poor in the UK is as least as high today as it was just before the start of the second world war. Another paper says the top 0.01% – those with declared taxable pay of £2.2m or more – have seen their share of overall income triple since 1995, and have weathered the financial crisis of 2008. The great triumph of the rich is that people like Mr Johnson have persuaded the average person to vote against taxes on wealth, such as inheritance tax and levies on property. If he wants to convince people that his words in 2015 meant anything, then Mr Johnson will have to change course in 2019.

• This article was amended on 29 July 2019 to add text to clarify that current average earnings are £5 less per week than in 2008.