"Pope Francis has said of his own accord that I can continue to wear my habit," the 79-year-old told journalists in the Vatican.
"The fact that religious men have to dress all in red as cardinals is very new," said Radcliffe. "I feel more like myself in my white habit."
At the ceremony in St Peter's Basilica on Saturday, the Dominican and Archbishop of Algiers, Jean-Paul Vesco (62), also wore the white habit.
The Indian bishop George Jacob Koovakad (51), the Pope's travelling marshal, received the cardinal's insignia in his black priest's habit, while Bishop Mykola Bychok (44) from the Ukrainian eparchy in Melbourne wore the wine-red cloak appropriate to his ecclesiastical tradition.
Nice quiet retirement life is gone
The College of Cardinals, which as of Saturday comprises 253 men from all over the world, is not a homogeneous group, Radcliffe said.
"The Pope wants an advisory council that reflects the enormous diversity of the Catholic Church. That means surprises are certain." The world is also facing fundamental changes, said the religious. "In 1989, the Berlin Wall fell and we thought the whole world was on the way to a Western free democracy - far from it."
Today, countries such as China, Russia and India are stepping forward.
"The big challenge for the whole world now is what vision we choose for humanity - it certainly won't be a Western one." In a world full of war, violence and social injustice, the Church as a global institution is called upon to set an example of hope, said Radcliffe.
Within the church, the most important thing is for women to be heard more, which is happening more and more, the theologian said. "There are so many female theologians, including in the Vatican. That's wonderful!"
He is still amazed at his appointment as cardinal, said the religious. "Three and a half years ago, I was seriously ill with cancer and didn't even know whether I would survive an operation," he reported. "After the operation, I thought I could now have a nice quiet life as a pensioner. But suddenly I'm back in the thick of things. I have no idea what that means for the future. I will serve the Pope, whatever he expects of me."