Geoffrey Boycott said he feared Alastair Cook could be "hounded out" of the England captaincy after the team's 100-run defeat by Sri Lanka in the second Test at Headingley on Tuesday.
After their 5-0 Ashes thrashing in Australia, England installed a new managing director in Paul Downton, a new head coach in Peter Moores, and a new chairman of selectors in James Whitaker.
However, all three insisted it was vital Cook remained as England captain.
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"Downton, Whitaker and Moores have hung their hats on him taking England forward, so if they were to sack him so quickly after all they have said about the new era, it would be embarrassing for them.
"They can be as supportive as they want and he can be as stubborn as he wants but if he fails with the bat in the first Test against India at Nottingham, which starts on July 9, and we lose again, then public opinion and the media will be so vocal he may be hounded out."
After the match, Cook insisted he had no intention of resigning as captain even though 24 innings have passed since the opener scored the last of his England record 25 Test hundreds.