Depending on the borough, there are different systems.
Tower Hamlets, Hackney, Lewisham and Newham have directly elected mayors. If a woman is elected to this position (eg Rokhsana Fiaz in Newham at the moment), she is still called the mayor.
Other boroughs have ceremonial mayors/mayoresses/mayoral consorts, usually drawn from the ranks of local councillors for long service etc. They have no executive power as part of this role apart from a charity fund that they can divvy out. When this role is filled by a woman, they’re usually referred to as ‘Madam Mayor’, but not always.