Dave Richmond from St Leger Homes said requests for help have rocketed since the start of the pandemic.
Speaking at a recent scrutiny meeting, where councillors grill department bosses across the local authority, Mr Richmond said many people are requesting help just before or on the day they are being evicted.
He urged people in difficulty to contact them sooner in order to better help people in precarious housing situations.
The St Leger Homes boss said the service in recent weeks had 13 people present as homeless in just one day.
But when they were offered emergency accommodation through hostels and other provisions, they turned it down.
Latest figures show there were 273 full duty homelessness acceptances in April 2020 to December 2020. But in the same nine month period in 2021, there was 292.
St Leger also takes part in mediation work where situations arise when young people ask for accommodation due to a family breakdown.
The organisation says they now operate an out of hours and weekend service so they can help more people, whatever time of the day residents fall into difficulty.
Mr Richmond said: “We’ve seen a four-fold increase in the number of people who feel that they are going to become homeless – this has been at level for the past year or so. This is a massively significant number.
“However, while a lot of people approach us in the early days, a number of people approach us on the day they are being evicted.“A large number of our staff are dealing with people who become homeless or will be in a week or so.
“What we have to do if we are to get out of this position, is to get back up stream and be able to help people earlier to prevent homelessness. When we can do that, it often becomes a successful outcome.
“We do need most people to deal with the problem themselves, perhaps with a little bit of support and advice so we’re looking at commissioning a new database and website giving advice on how to help.”