O'Reilly, who entered the Society of Jesus in 1987, said that he had moved out of his community because his work made him a contagion risk and moved into private accommodation.
"I've been living a slightly Carthusian existence," he said. "I have my little cell and somebody comes along and leaves me my food and runs away again. In some respects it's been quite pleasant and quite prayerful."
The lockdown has prompted him to reflect on his priestly identity.
He said: "From a ministerial point of view, it's been interesting. Because one of the things is, when you can't administer the sacraments and you can't meet people, what actually do you do all day as a priest?"
He asked friends for advice and one told him: "Why don't you just do what you're asked to do when you're asked to do it?"
"And I thought: 'Yes, that is actually the answer,'" O'Reilly said, "because everything that happens to you as a priest is in the passive mood: you are called, you are chosen, you are ordained, you are sent. Everything is in response to a need expressed by others, and I think that's the way it should be."
"And so for this period of time -- which I think will be long rather than short -- I think that, in the ministerial priesthood at least, it will require a great deal of listening to where those needs are and how they are expressed and how they may best be served."
O'Reilly expects the number of people sleeping on London's streets to increase significantly in the coming weeks -- and not only because hotels will cease to house the homeless.
"One of the other things that's going to happen is that because of the rapid economic collapse, particularly in the hospitality industry, we're going to get lots and lots of people who will lose their jobs, lose the accommodation that they have and will therefore be new rough sleepers," he said.
"I think that's going to be a big theme within a short period of time."
But he remained hopeful because of the improvements he had seen in the long-term homeless.
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"So many of my patients that I've known for so long are so very much better than I've ever seen them before. That always gives you a bit of a lift. You hope that at least some of that will be retained," O'Reilly said.
"All of life for our population is a bit 'two steps forward, one back.' This has been two steps forward. Let's see how much of that we can retain."