Peacock, 35, captained the Lions in their last test back in 2007, before the home countries were split ahead of the 2008 World Cup.
He said: “If you had Great Britain playing every four years, you wouldn’t see that.
“And then once every four years, you get together for Great Britain. These guys will play in a strong side against Australia.
“Great Britain is an unbelievably big brand … hugely after the Olympics … and should be brought back, not every year but every four years.”
Great Britain won their last four matches, back in 2007, culminating in a whitewash series victory over New Zealand.
Back when the split was announced, it was hinted that the Great Britain team would return for tours Down Under, something that hasn’t happened to date, although England did play in the Four Nations in the southern hemisphere in 2010.