But his actions have failed to stem a steady drumbeat of calls for his resignation, with some lawmakers saying his position is untenable if he lied to parliament, a matter under investigation by parliament's Committee of Privileges.
Ministers say he has not misled parliament.
Gray's report follows new revelations of what went on inside Downing Street when coronavirus rules meant people could not socialise outside their households or even, in many cases, attend funerals for loved ones.
Late on Tuesday, the BBC's Panorama programme cited insiders as saying staff crowded together at such events, and how, sometimes in the morning when arriving for work, they were met with bottles littering parts of the building. Some parties went on so late, they said, some people ended up staying all night.