The pair met for dinner in the Red Rooster restaurant.
Lord Bew insisted that the review was not prompted solely by the Osborne case.
Jeremy Fleming led the intelligence agency’s preparations for the London Olympics in 2012.
Foreign Secretary Boris Johnson announced the appointment of Jeremy Fleming.
Shadow foreign secretary Emily Thornberry said Turkey is a “vital ally, partner and friend” to the UK.
The former Chancellor has defended his new role amid criticism from fellow MPs.
He also used the visit to Israel to seek to boost trade as part of the Government’s drive to build international links ahead of Brexit.
Johnson is the first UK Foreign Secretary to visit Cairo since 2014.
The Foreign Secretary is anticipating a “fantastic free trade deal” being struck under Article 50.