John Reid, the health secretary, proposed the move as the Government drew up plans to curb junk-food ads aimed at children.
But he has backed down after being warned by his civil servants that penalising agencies for their private-sector work would breach Whitehall rules.
Instead, ministers will adopt a "softly, softly" approach under which they will urge agencies working for government departments to "think responsibly" about targeting children for other clients.
Reid had hoped to take tougher action because of a precedent set in the 90s, when the Department of Health refused to use shops that worked for tobacco companies. His plan was opposed by the Advertising Association.
One Whitehall source said: "We have looked into it but it's not possible. We would get into difficult waters if we start to make judgments about agencies based on their other work. We have to judge each campaign on its merits and pick the best people to do it. But we will be reminding agencies that they have wider responsibilities."
Reid had wanted the plan to be included in last month's White Paper on public health but it was omitted on the advice of civil servants. Instead, he proposed a voluntary code including a 9pm watershed for junk-food TV ads as well as curbs on press and poster ads.