Critics have accused the BBC of holding a left-wing bias and fostering a negative attitude towards former Conservative prime minister Margaret Thatcher.
Thompson, who started at the BBC in 1979 as a production trainee, accepted that the corporation's journalists did previously hold a bias towards politics from the left.
Speaking to the right-of-centre New Statesmen magazine, he said: "In the BBC I joined 30 years ago there was, in much of current affairs, in terms of people's personal politics, which were quite vocal, a massive bias to the left.
"The organisation did struggle then with impartiality. And journalistically, staff were quite mystified by the early years of Thatcher."
However, Thompson said that a "completely new generation" of journalists now works at the BBC meaning that there is "much less overt tribalism".
"It is a broader church. The BBC is not a campaigning organisation and can't be, and actually the truth is that sometimes our dispassionate flavour of broadcasting frustrates people who have got very, very strong views, because they want more red meat," he said.
"Often that plays as bias. People think, 'Why can't they come out and say they are...?' And that can play out on left and right."
Elsewhere in the interview, Thompson also discussed how his Roman Catholic faith has shaped the way he runs the BBC.
"I have lots of colleagues at the top of the BBC... of religious belief, [but] quite a lot with no religious belief at all and quite a few committed atheists. I think they've all got values they can bring to work," he said.
"I do think the BBC is very much - sometimes, frankly, almost frighteningly so - a values-driven organisation.
"People's sense of what's right and wrong, and their sense of justice are incredible parts of what motivates people to join. I'm part of that. For me, that's connected with my religious faith but the key thing is: you don't have to be a Catholic."