Ace Europe has moved its property, casualty, accident and health teams to the London Underwriting Centre, after outgrowing its Lime Street premises.
It will keep its multi-national, FTSE 500 and senior executive teams at its offices at 2 Minster Court.
The new office at 3 Minster Court in Mincing Lane will initially house 34 staff members but numbers are expected to grow.
However, an Ace spokeswoman denied the move was connected to talk that the company planned to pull out of Lloyd's.
“There's only so much space at our old offices at Lime Street and, as the accident and casualty team is growing, rather than split the over two buildings, they've got a building of their own,” she said.
Both the International Underwriting Association and the London Processing Centre are based in the centre, where about £3.5bn is written every year.