The surprise backing of the employers for a solution so close to the Labour plan delighted senior Labour sources and is likely to be interpreted as a snub to Ian Lang, president of the Board of Trade.
A draft policy document to be put to Labour's policy forum later this month proposes setting up a single investigatory authority to oversee competition and consumer policy, while converting the MMC into a powerful appeals body to hear disputes about its decisions.
This proposal was endorsed by Labour's joint policy commission on Tuesday, the day the CBI called on the Government to set up what amounts to the same structure - a single competition authority with the MMC losing its investigatory powers and becoming an appeals body.
A senior Labour source said: "We welcome the fact that the CBI is thinking along the same lines as Labour on these issues. We have consulted widely and we are determined to get the policy right."
The CBI said: "We are determined to be neutral and we take each issue as it comes. This is certainly not an attempt to curry favour with either side - this is what our members think on the issue."
Neither Labour nor the employers appeared to be aware until this week of how closely their competition policies had evolved in recent months.
Last year Mr Lang urged industry to abandon its long standing policy of political neutrality and support the Government on industrial and economic policies, but its approach to competition policy is bound to create new frictions.
Labour and CBI are also singing the same tune on reform of legislation against companies that abuse market power, with both suggesting a move towards the tougher approach of Article 86 of the Treaty of Rome, but adapted to UK law.
However, in one area, the control of takeovers, Labour's new document has stuck to a controversial proposal that the burden of proof should be shifted so that bidding companies must prove a merger will be in the public interest. This is opposed by the CBI.
Labour's draft, seen by the Independent, says the functions of the OFT and the MMC should be combined in a Competition and Consumer Standards Office "thus avoiding the duplication of investigatory functions and reducing considerably the time taken to carry out investigations". The CBI also cited the elimination of duplication as a reason for change.
A single competition authority has been on the Labour policy agenda since at least last summer. But Labour's policy-makers have tackled criticisms that this body would have too much power with their new proposal that the "MMC, or an organisation designed to replace it, might be empowered to act in concert with the Secretary of State as a powerful appeals body".
It would review decisions of the Competition and Consumer Standards Office and hear appeals on matters such as utility regulation.
The CBI also says the Monopolies Commission would be stripped of its investigatory powers and its job would be to hear appeals from a new competition authority, responsible for all the investigatory work now done by the OFT and the MMC.