After being proposed in July, the probe, will investigate into the lack of smaller competitors to the “big four” High Street names and the difficulties customers face in switching banks.
Also lending to small and medium-sized business will be looked in to.
Some of the large banks have labelled the probe as unnecessary.
In a submission to the CMA, Barclays said it felt the review was “not appropriate at this time”.
“Various developments, innovations and stimuli are changing the competitive landscape in relation to both [personal current accounts] and [small and medium enterprises] banking, and these must be given time to mature,” it added.
The competition inquiry will take 18 months to complete. The CMA also said it would review the 2002 report by its predecessor, the Competition Commission, to see if its findings were still relevant.