The inquiry also follows a round of shareholder revolts at annual general meetings this year, as investors took umbrage with the exorbitant awards given to top bosses.
May has signalled support for annual binding votes on pay packages, as well as employee representatives on boards.
Institutional investor Legal & General has written to all FTSE 350 chairmen to highlight a series of changes to pay practices that it wants to see adopted.
It has called on remuneration committees to consider retendering contracts for pay consultants — after a revolt by more than 20% of shareholders — and publishing statements on how committees can tackle concerns.