The full figures will be revealed at a Downing Street event on Wednesday, where Davies is expected to announce that nearly one-third of FTSE 100 appointments since he published his report on gender equality in February have been women.
However, a number of women held up as evidence of success already hold directorships, so cannot be counted as representing a new stream of female talent, argue City commentators.
Vanda Murray, who was last week announced as a non-executive director of defence firm Chemring, is currently non-executive director of construction company Carillion and Manchester Airport Group.
Witts will become a non-executive director of builders’ merchant Wolseley on 1 November alongside her role of chief financial officer for Vodafone Group for Africa, Middle East and Asia Pacific, through which she is a non-executive director of Safaricom.
In December last year, the most recent Female FTSE Index report from Cranfield School of Management showed that 14 per cent of FTSE 100 board posts are held by women.