As a result, it says, consumers buying from other companies could end up paying higher prices.
"We have set out ground rules for how sites should behave, as well as being clear on how regulators can ensure people have a better experience online," says CMA chief executive Andrea Coscelli.
"We are also taking enforcement action where we suspect the law may have been broken."
It has the ability to fine offending companies up to 10% of their turnover.
On the whole, says the CMA, the vast majority of people who use price comparison sites are happy with the service they receive. But, it says, there's room for improvement.
It wants sites to be clearer about how they make their money, how many deals they're displaying and how they are ordering the results. Companies often pay to appear in lists, or to be pushed up the rankings, and the site may get a commission when you switch providers.
It's also important to remember that not all companies appear on all comparison sites; some aren't listed on any.
"Try more than one site, or another one next time - they're all different," says the CMA. "Check how many companies they cover. Some sites will show more than others."
Its research shows nearly two-thirds of people using a price comparison site do visit more than one when shopping around.
"If you want more info, look for sites that show reviews and product features. Watch out for adverts mixed in with the results," continues the advice. "Don't forget to visit the sites of businesses not included on the comparison website."
The CMA says it now plans to turn its attention to how well consumers are protected when it comes to car hire companies and hotels.
Top Ten Weirdest Holiday Home Insurance Claims
Top Ten Weirdest Holiday Home Insurance Claims
The owner of a holiday home in Spain returned to inspect his property after he had let it to a group of young people in their 20s for two weeks, to find that they had created an indoor beach including sand and water to emulate the sea. The youngsters explained that the local beach “hadn’t lived up to their expectations”.
A slightly oblivious swan didn’t see what was coming his way. It was flying happily through the air, completely unaware of a set of high voltage power cables in its flight path which it duly hit. The swan had the shock of its life and dived straight for the roof of a holiday home underneath, crashing through the roof and leaving a massive hole in need of fixing.
At a holiday home in France, a cow walked over a swimming pool cover. As the cow was considerably heavier than the cover could hold, the cover broke and the unsuspecting cow took an involuntary dip in the pool; resulting in considerable damage to the pool and the need for a winch to rescue the distraught bovine.
Holiday guests staying in a Spanish property moved items of furniture from inside the holiday home they were renting, including a sofa, single bed and chest of drawers, into the shallow end of the swimming pool. The guests had been under the influence of alcohol when they’d decided to rearrange the furniture in such a way and claimed they "couldn’t remember" why they had done it.
A particularly passionate couple managed to not only badly scratch the wooden floor of their bedroom by causing the bed to move vehemently, but also caused the bed to break, as well as the bedside lamp and bedside table. The couple explained that all damage had been caused during one session of lovemaking and they apologised profusely.
Following a rental, a holiday home owner made a gory discovery; he found blood splattered all over carpets and walls. After further investigation, he discovered a makeshift cardboard coffin containing a pig’s head in the bin, suggesting that a sacrifice had taken place at his property.
A young couple tried to pursue a claim against the owner of their holiday apartment in Spain on the basis that both bed sheets and towels were "too hard" and caused scratches and irritations on the skin, which prevented them from using the pool and sunbathing comfortably.
A holiday cottage in Devon needed completely redecorating after the holiday guests had decided to have an indoor barbecue on the flagstone floor, as ‘the weather didn’t allow for having it outside’.
One unsuspecting holiday property owner in Italy was shocked to find out that his house had been turned into a brothel by his guests during a four week rental period, resulting in the need for a deep clean and replacement of soft furnishings.
A lady in her late 30s from Manchester sought compensation from the owner of her holiday home in Marbella as the gravel on the driveway "had wrecked" four pairs of her designer stilettos and forced her to replace them with new ones.