"They are well over half way through and now very firm in the northern parts of the city," Chalmers stated in a briefing.
The deputy commander, who is also a member of the British Army, added that the Iraqi military still has got "a while to go."
"But still it is going to be far quicker than we probably had estimated a couple of weeks ago," he added.
Fallujah, located some 42 miles west of the Iraqi capital Baghdad, is one of the largest cities in the Anbar province. Daesh has been in control of the city since 2014.