Researchers Andrew Pollard, Peter Horby, Martin Landray, Catherine Green, Teresa Lambe and Adrian Hill are among those also honoured.
Professor Gilbert becomes a Dame Commander of the Order of the British Empire for her key role in creating the jab, which has gone into the arms of tens of millions of people around the world.
Public Health England estimates the vaccination programme has prevented 42,000 hospital admissions and more than 14,000 deaths in older adults in England alone.
Venture capitalist Ms Bingham is similarly honoured after overseeing the acquisition of the millions of vaccine doses now giving hope to the nation that the fight against the virus is being won.
She hailed the efforts to develop jabs as "a triumph of scientific and industrial collaboration".