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The head of the International Monetary Fund has warned that a persistent violation of ethics among bankers and rising inequality pose a major threat to growth and financial stability.

Christine Lagarde told an audience in London that six years on from the deep financial crisis that engulfed the global economy, banks were resisting reform and still too focused on excessive risk taking to secure their bonuses at the expense of public trust.

She said: "The behaviour of the financial sector has not changed fundamentally in a number of dimensions since the crisis. While some changes in behaviour are taking place, these are not deep or broad enough. The industry still prizes short-term profit over long-term prudence, today's bonus over tomorrow's relationship.

"Some prominent firms have even been mired in scandals that violate the most basic ethical norms - Libor and foreign exchange rigging, money laundering, illegal foreclosure."

Lagarde warned the too-big-to-fail problem among some of the world's largest financial institutions was still unresolved and remained a major source of systematic risk, with implicit subsidies of $70bn (£42bn) in the US, and up to $300bn in the eurozone.

In a speech littered with quotations from Winston Churchill to Pope Francis and Oscar Wilde, Lagarde said international progress to reform the financial system was too slow. "The bad news is that progress is too slow, and the finish line is still too far off. Some of this arises form the sheer complexity of the task at hand. Yet, we must acknowledge that it also stems from fierce industry pushback, and from the fatigue that is bound to set in at this point in a long race." Lagarde told the inclusive capitalism conference that rising inequality was also a barrier to growth, and could undermine democracy and human rights. The issue has risen up the agenda in recent months with the publication of the French economist Thomas Piketty's book, Capital in the Twenty-First Century.

"One of the leading economic stories of our time is rising income inequality, and the dark shadow it casts across the global economy," Lagarde said.  Borrowing from Oxfam research, she noted that the world's richest 85 people, who could fit into a single London double-decker bus, control the same wealth as the poorest half of the global population of 3.5 billion people.

Options to address inequality include more progressive tax systems and greater use of property taxes, she said.

"We must recognise that reducing inequality is not easy. Redistributive policies always produce winners and losers. Yet if we want capitalism to do its job – enabling as many people as possible to participate and benefit from the economy – then it needs to be more inclusive. That means addressing extreme income disparity."

Lagarde compared the rising awareness of social responsibility tied into the financial system with the world's expanding environmental consciousness. "Just as we have a long way to go to reduce our carbon footprint, we have an even longer way to go to reduce our 'financial footprint'. Yet we must take those steps."