The council has already spent £200,000 on setting up Move51⁰ North.
Labour mayoral candidate Sadiq Khan has promised to set up a London-wide agency along the same lines.
A Move51⁰ spokesman said the agency was "at the very early stages of setting up" and operating to target.
'People before profit' Move51⁰ is the first lettings agency to be set up by a borough council. It aims to "put people before profit" by offering tenants good homes at reasonable rents, with vetted landlords.
Launch of Move 51 Degrees North
As well as attracting tenants in the private sector, Haringey wants to be able to offer assured shorthold tenancies and temporary accommodation to people at risk of homelessness.
Sadiq Khan promises to set up "a London-wide not-for-profit lettings agency for good landlords, building on the work that councils have started, and ending rip-off fees for renters".The agency, a strand of Homes for Haringey - which runs the council's housing stock - began trading on 6 October and was "introduced to landlords" at an event in the same month.
It launched a poster campaign on the Tube network at the beginning of November.
A director, junior consultant and property manager were hired last summer, with the latter job offering a salary of £30,000 plus a guaranteed £5,000 bonus in the first year.
Move51⁰ then organised a "launch event" on 10 March.
A spokesman for the agency said: "The business is financially operating to target."
In total, Haringey expects to spend an additional £1.37m on the agency, but expects the agency to make a surplus by 2019 and to cut the amount the council currently pays private landlords to meet its housing obligations.
One-off funding would be needed if the agency decided to buy up local lettings agencies or Right to Buy properties, the report said.
Haringey cabinet member for regeneration and housing, Councillor Alan Strickland, said: "We only publically launched Move51⁰ six days ago and it would be ridiculous to rush to sign up any landlord or tenant without doing proper checks to deliver a service that people can trust.