The US has lent its backing to Britain to protect the City from losing trillions of pounds of complex financial derivatives business after Brexit, warding off a potential banking industry land grab by the EU.

In a joint announcement heralded as a sign of the special relationship between the UK and the US, the two countries said they would take every step to ensure the continued trading of derivatives across the Atlantic under every Brexit eventuality.

Derivatives are financial contracts widely used by companies to manage risks, ranging from hedging against changes in central bank interest rates to fluctuations in commodity prices. Brexit threatens to unpick trading in the UK, even with the US, as City banks currently operate under EU rules while Britain is a member of the bloc.

Under the steps announced by the Bank of England, the Financial Conduct Authority and the US Commodity Futures Trading Commission, firms working in the US and the UK will continue to meet the requirements required to operate in both countries, even if Britain leaves the EU without a deal.

London and New York sit at the centre of the world’s multitrillion-pound derivatives market, with the US and the UK controlling 80% of the $594tn (£454tn) a year business – worth more than five times world GDP.

About a third of the £230tn of derivatives contracts traded in the UK every year come from US companies, more than any other jurisdiction.

The development comes as Brussels prepares rules that would force clearing houses – financial institutions key to the trading of derivatives – outside the EU to come under the supervision of its regulators.

Designed as a response to Brexit – as the vast bulk of the EU derivatives trade is handled in London, outside of its control from as early as 29 March – the rules have been seen as a land grab for trading to move to EU cities such as Paris or Frankfurt. The EU’s plan has run into opposition from the US, which views the steps as overreaching its remit.

The new agreement between the US and the UK could help strengthen the City’s position as a leading global financial centre.

Although Brussels still plans tougher rules for the future, it also agreed this month to allow UK firms to continue trading EU derivatives in the event of no-deal Brexit, taking a major risk to financial stability off the table.

Christopher Giancarlo, the chair of the CFTC, said: “London is and will remain a key global centre for global derivatives trading and clearing for a long time to come.

“The bulk of the transactions take place across the Atlantic. Today is a statement of continuity of that cross-Atlantic trade.”

Mark Carney, the Bank’s governor, warned the relocation of EU interest rate swaps – one of the most common derivatives contracts – away from London to the EU could generate as much as €20bn (£17.4bn) in additional costs.

“That’s borne ultimately be savers, by businesses, by the real economy. It flows through the participants in these markets,” he said.