The FTSE 100 firm said that over the next few years the focus will be on supporting customers during the economic crisis caused by COVID-19 and a continuing low interest rate environment.
However, Cheshire told the board “he is unable to accommodate the increased time commitment and duration required to see through this programme”.
The company recognised that Cheshire helped establish Barclays UK as a ring-fenced bank and successfully set up its board and governance structure.
He will be replaced by senior independent director Crawford Gillies on January 1, while Cheshire will remain on the board until the annual general meeting in May to ensure a smooth transition.
Gillies will remain on the Barclays board alongside his Barclays UK role.
Shares dipped 1% to 144.6p on Friday morning.