The Chancellor said “freedom, liberty and justice” would prevail despite her death and called for contact between constituents and their MPs to be preserved.
He was speaking at the Mansion House dinner where Chancellors usually discuss the economy and this year Mr Osborne was due to talk about next week’s EU referendum.
But in the wake of Mrs Cox’s death he scrapped the planned text.
Mr Osborne said: “One of the virtues of our Parliamentary democracy is the everyday accessibility of MPs to the people they represent.
“It’s what makes the way we govern ourselves very different from many others.
“To be an effective representative, all of us who are MPs engage with their communities, talk to everyone and anyone, hold constituency surgeries and must be prepared to stand up and argue publicly for what we believe.”
Mr Osborne said the Batley and Spen MP’s death was a moment to “reflect on and hold to the values that are the foundation of this great nation”.
He continued: “We believe in freedom, liberty and justice.
“People are free in this country to live their lives as they choose and express themselves without fear. Society will protect their right to do so and hold to account those who disregard our laws.
“Today’s horrible events are an assault on all of these values.
“But we know that these values, no matter how they have been challenged in the past, have always prevailed, prevail today and they will always prevail. For they are the values of Great Britain, our great democracy.”