Ms Mayhew, who takes over today, is the first woman in this powerful post, Today said.
She said it was important to listen to the business and City community, if London is to keep its position as the leading international finance centre.
'One of the things that may be looked at, if we had a new government, is how to reform our voting system', she said.
Ms Mayhew said the City would continue to thrive when there is a single European currency, even if the UK does not join in. 'What we are gearing up to is to trade the euro against the yen and the dollar and other currencies', she said.
As representative of the City, 'We're spending a lot of time negotiating with the European Commission...to make sure that when the euro is traded it is traded properly, with proper legal continuity. We're doing a lot of the technical work behind the scenes for the trading of the euro', Ms Mayhew said.