Bidding for a rental is happening more too as renters fight it out to snap up a home.
One Trade Me listing for a two-bedroom rental had to be taken down only 25 hours after going up due to a deluge of 55 applications.
Jeffries said some landlords would shortlist possible tenants and then go back to them and ask what the highest rent they were willing to pay way.
It's a heavy blow on top of the jump in median rent - since October the average median rent has spiked $30 from $450 per week to $480 in December, to match the record set in January last year.
"We expect to see a new record price in January as the influx of university students heats the market even further," Jeffries said.
He believed the spike in cost would reach about $50.
The rent spike is driven by a combination of factors including a lack of housing, first time buyers staying in their rentals longer while they save a deposit and the influx of people coming into Wellington, he said.
"There's also an argument that the Government's increase of the student allowance has been a contributing factor. I'm not so sure that's having an impact, this is a simple supply and demand equation - demand is far outstripping supply and the market is reacting with higher rents."
Wellington's situation is grim compared to the rest of the country. Nationwide the number of rentals has dropped by 49 per cent on December 2016.
The median weekly rent rose 2.2 per cent to $460 a week.
"Wellington is a bit of a standout . . . Wellington has a very concentrated employment market and people like to live close to where they work, hence we get this demand particularly around the central suburbs."
"While it is common for us to see the median rent increase in December, it doesn't usually
increase this much. The market is much tighter than usual and it is highly likely that tenants will be asked for record rents in January and February all over the country."
Some landlords were also leaving the market as regulations around rentals became stricter.
"Overall, the shortage of rental properties isn't going to get easier anytime soon. Demand will continue to exceed supply this year and as a result we are predicting that the national median weekly rent will rise between 3 and 5 per cent."