Colonel Chris Vernon also said the last five days of fighting had made it impossible to get aid into the area.
“Basra (is) clearly nowhere near yet in our hands and we have no way at the moment of getting humanitarian aid into Basra,” he admitted on Sky News.
“But clearly, as we begin to pressurise Basra and to begin to dominate it militarily we should move towards the day we can get humanitarian aid into Basra.”
The colonel said fighting had taken place on the outskirts of the city.
But allied troops had not gone into the city centre “for worry of collateral damage”.
He said: “The key to Basra is to eradicate the Baath Party control and the irregular forces operating under their control there.”
By doing so, the “hearts and minds” relief operation could then be put in place for the civilian people on the ground.
“Not easy, no time lines on it, but that’s what we are working towards,” he said.
The colonel said he was confident they had enough British troops based in southern Iraq.