Damazer, who left the BBC this autumn to become head of St Peter's College at Oxford University, has been awarded a CBE for services to broadcasting.
He departed Radio 4 with the station in rude health, enjoying an average weekly reach of 10.4 million listeners and a 12.5% share of the total audience.
Discussing the CBE award, Damazer told The Guardian: "I'm very pleased, but I don't delude myself. It's not specifically for me but much more recognition of the role that Radio 4 plays in national public life.
"I was the fortunate person able to do a bit of choreography, but the real achievement comes from the people who make the programmes and come up with the ideas."
BBC controller of audio and music Tim Davie said that Damazer was an "outstanding controller" of Radio 4. Davie added: "He left a legacy of many brilliant programmes as well as a buoyant network. I am sure that everyone involved in radio will be incredibly pleased that he has been recognised."
Lloyd was also awarded a CBE for services to broadcasting, after a career spent producing acclaimed comedy shows, such as Blackadder, Spitting Image and Not The Nine O'Clock News.
Veteran newsman Gall was given the CMG order of St Michael and St George for his charity work in Afghanistan. He founded Sandy Gall's Afghanistan Appeal (SGAA) to treat disabled people in the country.
Elsewhere, former head of the BBC's science unit John Lynch was awarded an OBE for services to broadcasting and Ellis Rich, the outgoing chairman of the Performing Right Society, was given an OBE for services to the music publishing industry.