"We will have people who are extremely ill, whose place of shelter will be St Peter's, or the doorways that they sleep in."
The church, built in 1878, has a long history of helping the homeless community, or as Archdeacon King describes "the least, the last and the lost".
"We have that discussion about people hunkering down and isolating themselves until the illness passes. For some people there is nowhere and so what happens to them?"
Archdeacon King said rough sleepers already struggle to exercise precautions such as sanitising and social distancing.
And he adds that, even if accommodation was made available for self-isolation, continuing to care for people in that situation is a problem.
"That works fine for us if we have a partner or a parent or a child who can help us do that and recover. For those that don't have that, where does that help come from?"
He said it will not come from hospitals, because they will be at capacity.
Archdeacon King said Government agencies need to equip and train volunteers to continue services if there is a lockdown period.
Plans are brewing, he said, but he is concerned about how it will play out.
"There are so many things being planned for at the moment as we head further into this crisis, that I just don't want to see that the most vulnerable miss out on the plan."
Up in central Auckland, Lifewise's Peter Shimwell said they are giving their street whānau phones and sim cards to make sure they do not become disconnected.
He said Lifewise is a face-to-face service, so there is concern over how to maintain those connections with people so they are not "left behind and further disconnected".
"At times like these we need to think outside of the box, in terms of city hotels and whether we have the capacity to unlock some of those."
Stephanie McIntyre of DCM - another Wellington faith-based group working with rough sleepers - said it is an indictment on New Zealand's society that people are even in this position.
"The upshot of that, is that in this environment now, when we really need people to be safely home in their houses, we've got a very vulnerable group in our population, who are community members and might literally be left out in the cold."
All the community organisations hope that empty motels will be opened up for rough sleepers to self-isolate, if need be.
McIntyre said that now is not the time to be worrying about growing motel bills.
She said that DCM is also checking to see if people have phones and can provide one if needed. But she hopes the Ministry of Social Development will ensure people do have a phone and sim card, so that they can be contacted.
Wellington City Council's Manda Grubner said the council is concerned about how Covid-19 will affect the homeless community.
"It's very difficult to maintain hygiene and do the things we are telling everyone to do, such as stay home."
She said the council is reaching out to agencies working directly with homeless communities, including food distribution organisations, to figure out what support they need.
Grubner said the council has implemented its emergency welfare response and has had "all hands-on-deck" calling hotels to see who could accommodate people.
Auckland Council's Christine Olsen said the council is mindful that people rough sleeping often have more health problems than the rest of the public.
She said it is working with agencies closely and considering making toilet and washing facilities available, as well as charging stations to keep phones charged.
Olsen said the council has talked with the City Mission to come up with contingency plans including to ensure the daily meal, which feeds between 300-400 people a day, is still provided.
Meanwhile in Auckland, Auckland Action Against Poverty spokesman Ricardo Menendez March called on the Government to address the emergency housing shortage.
"People who are in inadequate, overcrowded homes or are living in the streets can't follow the directives laid out by the alert level 4 to Covid-19.
"If we do not provide access to adequate housing to everyone who needs it, we are dooming thousands of people who do not have the means to self-isolate.
"We can prevent countless of infections and deaths from within some of our most at-risk groups by providing them with safe homes."
The Government had all the tools to ensure that everyone has a safe place to live, he said.
"We already have more than twice the number of empty homes in Auckland as there are families on the housing waiting list.
"We are urging the Government to acquire ghost homes, build enough public housing and introduce rent caps to ensure no one is left behind in our response to Covid-19."
The Ministry of Social Development is urging anyone sleeping rough to get in touch.
In a statement, MSD spokesman George Van Ooyen said "nobody needs to sleep rough, and every day we provide emergency accommodation for those in need, including those who have been sleeping rough".