By Huw Jones and Carolyn Cohn

LONDON (Reuters) - U.S. insurer AIG <AIG.N> may move its European headquarters from London to another European Union country because of Britain's vote to leave the EU, the head of the AIG's European and UK operations said at an industry conference on Tuesday.

AIG joins a growing list of finance industry companies that have said they may have to shift some operations to continental Europe to maintain links to customers after Brexit.

Speaking at the same conference, trade minister Mark Garnier said the government was listening to the financial industry's concerns over Brexit. "We will aim to limit uncertainty surrounding business," Garnier said.

"The government fully understands the implications of Brexit for the financial services industry," Garnier told insurance trade body ABI's annual conference.

Banks, insurers and asset managers in Britain fear losing access to the EU's single market, and a damaging "cliff edge" effect of leaving the bloc if there are no transitional arrangements ahead of any new trading terms agreed with the EU.

Anthony Baldwin, chief executive of AIG's European and UK arms, said the group might decide in the coming year to move its European head office from London to an EU country after Brexit, though it would still maintain a big London hub. AIG has around 2,500 staff in Britain.

Baldwin told reporters on the sidelines of the conference he was looking at half a dozen locations, including Dublin, though the impact on staffing would not be material if the headquarters moved out of London.

"At a certain point in time you have to pull the trigger in the absence of any clarity on where negotiations are going with the transition period," Baldwin told the conference.

"We will always continue to have a big London hub but we might have a European headquarters elsewhere," he said.

Baldwin said AIG has experience of moving operations after shifting its European head office from Paris to London five years ago. About a couple of hundred jobs were moved.

"We know what it takes," Baldwin said, adding the process had taken around 18 months.

The Lloyd's of London insurance market, underwriters Hiscox <HSX.L> and Beazley <BEZG.L>, and motor insurer Admiral <ADML.L> have also said they might shift operations from London to centers like Dublin.

Huw Evans, director general of the ABI, said the insurance industry should not moan about the Brexit vote, but instead engage with politicians to find a way forward and minimize risks to the sector.

British Prime Minister Theresa May has said she will start formal divorce talks with the EU by the end of March.

"That timetable has not changed," Garnier said.

(Reporting by Huw Jones, editing by Carolyn Cohn and Jane Merriman)