The City of London, home to the U.K.’s largest trading and financial services, is suffering from a loss of professional talent due to Brexit, warns a U.K. job recruitment agency.

“The City is still haemorrhaging talent because of Brexit, and we risk losing jobs, too,” said Hakan Enver, operations director at recruitment consultancy Morgan McKinley Financial Services, in a press release published Tuesday.

The latest London employment monitor for July revealed the number of jobs and job seekers in the City, London’s financial center, grew for the fourth consecutive month. The number of jobs available increased 1 percent month on month, compared to a decrease of 14 percent in the same month last year, while the number of professionals seeking jobs increased 12 percent.

However, over a year the number of professionals seeking a job in the financial capital is down 33 percent, while the number of jobs available has shrunk 11 percent, due to the uncertainty weighing on the economy.

“Normally the City clocks out for July, but with the industry being swept from under them, people are scrambling to make the most of the time left in the EU,” said Enver.

“EU nationals who want to stay in Britain have a shrinking window of opportunity to get a job and permanent residency, and many are seizing it.”

The City makes a huge contribution to the U.K. economy. The most recent available survey found that in 2015 the City employed 1.5 percent of the U.K.’s total employment and contributed £48 billion ($62 billion), or around 3 percent, in gross value added to the U.K.’s national income.

But with the future trading relationship of the U.K. and the European Union still to be negotiated, many financial firms are putting off job recruitment or are preparing to open offices within the EU.

For instance, asset manager Standard Life is considering Ireland as its European base for when the United Kingdom leaves the EU, its CEO told CNBC on Tuesday. Other firms have announced similar plans: Bank of America announced in July it would move some roles to Dublin, while HSBC will relocate 1,000 roles to Paris.

“The language has changed. Employers and employees used to talk about ‘if’ they had to leave London. Now they’re talking about ‘when’ they leave London,” added Enver.

The report comes as the U.K. Brexit minister Davis Davis outlines the government’s proposal for an interim customs agreement with the EU, which would minimize friction on trade with the bloc after Brexit while allowing the U.K. to negotiate new trade deals elsewhere.

The government said this temporary agreement would allow for a smooth and orderly transfer to a new trading regime.

Gerard Lyons, chief economic strategist at Netwealth, said this temporary agreement would serve as a bridge for businesses.

“There’s been all this talk of cliff edged and that sort of stuff, but what we really have here is a different analogy. It’s a bridge: you can see what you’re getting on, you want to know how long the bridge is and where it’s going to take you,” he told CNBC’s Street Signs.

“And what we’re seeing proposed here is a bridge to counteract all those talks and fears of a cliff edge.”

Follow CNBC International on Twitter and Facebook.