The Competition and Markets Authority (CMA) had ordered all insurance companies to split out the extra charges for the additional protection.
But the Co-op was the only firm which missed a deadline to do so, in August last year.
As a result around 120,000 customers received quotations that were unclear.
From 1 February, the Co-op will provide two separate quotations - one with no claims bonus protection, and one without.
"It is very disappointing that a major company such as Co-op Insurance has taken so long to provide this vital information to its customers," said Adam Land, senior director of remedies, business and financial analysis at the CMA.
"Before the order came into force, the price and benefits of NCB [no claims bonus] protection were often unclear to drivers.
"We expect the Co-op to fully comply with the terms of our directions immediately, so that motorists can search more easily for the best deal for them, and decide whether or not they want this optional cover."
The Co-op said most of its quotations do now provide separate details of no claims bonus charges.
"For 90% of our new business customers we are already fully compliant with this order," a spokesperson said.
"We are part way through a major transformation programme, which when complete will allow us to be fully compliant and enable us to provide best in class service to our members."

Mohammed Ali Abboud is on trial for murdering Agnieszka Szefler at the home they used to share in Bridge of Earn, Perthshire, in January.
The jury were shown video footage of Mr Abboud telling detectives Ms Szefler "fell" with the knife in her hand.
The 57-year-old denies all the charges against him.
The High Court in Edinburgh heard Mr Abboud told officers that Ms Szefler's temper changed just before she had her period and that she often threw household items at him during this time.
He said the 27-year-old teacher sustained serious injuries during the struggle on 23 January.
He said: "She fell. She had the knife in her hand."
The video footage of the police interview was shown on the fourth day of proceedings against Mr Abboud, who also denies a charge of attempting to defeat the ends of justice by covering up his role in his former partner's death.
In the footage, a detective told Mr Abboud that he did not believe his claims that he did not murder Ms Szefler.
The policeman then asked the accused to admit that he murdered her.
But Mr Abboud said the pair got into a struggle and he was trying to stop her from causing any of them serious injury.
He said: "I was trying to stop her. It got out of hand."
Mr Abboud's lawyers have lodged a special defence of self defence.
The trial, before judge Lord Uist, continues.
The Co-op has been ordered to provide clearer insurance quotations, after it failed to tell motorists about separate charges for no claims bonuses.
[NEXT_CONCEPT]
A man accused of stabbing his ex-partner to death told police she came at him with a knife and they started to struggle, a court has heard.