Britain fully left the European Union last December but Brussels has yet to say whether it will grant market access for the UK's financial sector, John Glen told a Bloomberg event.
"In the meantime, we will continue to look at these opportunities and make judicious and well-founded changes."
Changes such as how much information should be disclosed on issuance of bespoke bonds "does not mean we are becoming the Wild West", Glen said.
Britain has not gone down a "deregulatory route" in financial services since Brexit despite some initial expectations, Glen said.
"We know our reputation globally rests on us having high standards, but that does not mean we can't do things differently," Glen said.
"We are certainly not complacent."
Brussels has said it is scrutinising how far Britain will diverge from EU rules before considering financial market access.
"Divergence will be in a framework, and the framework will be international standards," Bank of England Governor Andrew Bailey told the same event.
OFFSHORE CENTRE
Howard Davies, chairman of NatWest bank, said London would remain Europe's big offshore financial centre, though some domestic-focused European business would drift to continental financial centres due to Brexit.
"It's not been catastrophic, not disastrous, but it will reshape, and London needs to think of itself as being the intermediator for Europe versus the rest of the world, rather than trying to be an 'all things to all people' financial centre for the whole of Europe," Davies said.
The trickiest issue for Britain is pressure from some EU states to limit the ability of fund managers in London to run funds listed in the bloc, Davies said.
London asset managers pick stocks and bonds for EU-based funds worth 2.4 trillion pounds, helping to cement the British capital as a global asset management centre.
"That is the area government should be focusing on most and making sure that threat does not materialise... I've not any great evidence that they are," Davies said.
Stephen Cohen, head of EMEA at asset manager BlackRock said Britain made a mistake in not making the financial sector a priority in exit negotiations with the EU, and belated recognition of the sector's importance was a "little bit late".
Staff in London's financial district, where NatWest's head office is based, are returning to the office after working from home during the pandemic, helping to revive the city's streets.
But Davies expects a "hybrid" mix of home and office working to become the norm. "It's obviously not great for the sandwich bars around us," he added.
(Reporting by Huw Jones, editing by Andy Bruce and Gareth Jones)
By Huw Jones
