The firm - which owns brands including Churchill - said it had “proactively taken steps” to mitigate any impact, but added that it was not “immune” to a hard Brexit, given its exposure to financial markets and as it imports goods and services from the EU to fulfil insurance claims.
It warned that, in the event of a disorderly Brexit, the impact on the group could “correspondingly also be disruptive and potentially material”.
The comments came as it reported a 6.4% fall in operating profits to £601.7 million for 2018 as gross written premiums dropped 5.3% to £3.2 billion.
It also dealt a blow to staff as it offered no free shares this year - having handed previously handed out nearly £1,700 worth of free shares per employee since flotation in 2013.
The group blamed the fall in earnings on lower reserve releases and investment returns, while the drop also came despite a £55 million boost after changes to the UK’s Ogden personal injury discount rate change.
The annual results follow the announcement last week that boss Paul Geddes will be replaced by finance chief Penny James when he steps down in May after 10 years at the helm.
Announcing his last set of full-year figures, Mr Geddes said 2019 was a “pivotal year” for the group.
He added: “I am pleased to announce a strong set of results driven by our resilient business model which performed well in a highly competitive market.”
Results revealed that full-year statutory pre-tax profits lifted 8.1% to £582.6 million.