LONDON (Reuters) - The City of London financial district said job relocations to the European Union on Day One of Brexit remained far short of the hundreds of thousands predicted when Britain voted to leave the bloc over three years ago.

FILE PHOTO: Catherine McGuinness of the City of London Corporation, poses for a photograph in London, Britain, January 17, 2018. REUTERS/Hannah McKay

Catherine McGuinness, leader of the City of London, the municipal authority for the “Square Mile” financial district, said the number of bankers and insurance and asset management staff moving to EU subsidiaries was between 2,000 and 7,000.

“We really have not see any major Brexodus,” she told reporters on Tuesday. “We are not hearing signals of huge further moves.”

Britain formally left the EU on Jan. 31.

Britain and the EU have unveiled opening positions in talks for a new UK-EU trade deal they want in place next January after a “business-as-usual” transition period following Brexit ends.

Financial services may not be as “picturesque” as fish -- a reference to what will be a politically contentious sector in the talks -- but they are of critical importance to the UK economy, McGuinness said.

The EU has said that a deal on financial services will be linked to the overall results of trade talks.

McGuinness hoped Britain can improve on the financial market access terms known as equivalence that the EU offers to non-EU states like Singapore or Japan.

Under equivalence, the EU grants access if it deems that a foreign country’s financial rules are as robust as those in the bloc.

Additions could include close cooperation between UK and EU regulators, and more stable arrangements than the 30-day notice for withdrawing access.

McGuinness urged Britain not to retaliate if the EU limited financial market access.

“Our advice is to remain as open as possible,” she said.

McGuinness said there were no major calls in Britain’s financial sector to radically diverge from rules it has inherited from the EU to threaten equivalence-based access to the bloc.

“The big potential competitor to London is New York. We will remain Europe’s only global financial centre into the future,” she said.