The Blur frontman was introduced to the Labour Party leader as he wooed celebrities for their backing ahead of the 1997 general election, which Blair went on to win with a landslide.
However, Albarn felt increasingly uncomfortable in Blair's presence and eventually decided not to vote for him after picking up "something kind of odd" with his behaviour.
The singer tells Britain's Channel 4 News, "I met Tony Blair and I sort of, in a way, kind of had a premature insight into the sort of dark mechanics of politics, and at that point I honestly felt terrified about Tony Blair. I picked up on something kind of odd about him that I didn't understand. I was a bit scared of him, to be honest with you."