This can be particularly challenging for products which are delivered on a pan-European or international basis due to the different regimes in place.
Green suggested some groups may be pushed to consider whether to continue operating in the UK as a result.
However, she also thought it was possible that the EU would follow suit with its own consumer duty.
"The UK has long influenced the EU, particularly pre-Brexit, with its regulatory agenda. If you look at things like Mifid II, there were rules in there which had resonance with our Retail Distribution Review," she said.
Following implementation of the consumer duty at the end of this month, Green expects the FCA to carry out reviews in firms across different sectors as well as dissect annual self-assessments as part of its supervision strategy.
There are already consumer duty questions in current supervision, she said, although she doesn't expect such probes to be enforcement focused just yet.
carmen.reichman@ft.com
