The 2% increase, which comes in next month, follows a hike last year of 9.24% and comes at a time when diesel prices are about 20p less than a year ago and inflation is static.
John Lennon of the Association of News Retailing said the rises were "a stark symbol" that the newspaper distribution process is not working.
"Now that Dawson News has exited the market, a bad situation has been made worse," he said. "We are calling on the OFT to look closely at the threat that the monopolistic position of the two remaining wholesalers has on carriage charge increases and to give a clear view on how this will affect the interests of consumers. The best way to achieve this is through a competition investigation of the market."
One Menzies customer who asked not to be named said: "There's no justification for this increase in CSCs they know we have no choice but to swallow it. It's monopolistic bullying, pure and simple. If anything, their costs should have gone down now that News International is delivering its own titles in some areas."
A spokesman for Menzies said its customers were informed in January that a 2% increase was due but would be delayed for six months. "We remain committed to delivering the best possible service to our customers for the leanest possible cost," he said.
Menzies paid £500,000 for its share of Dawson's assets. Smiths News, the other remaining wholesaler, said its £1.5m acquisition of former Dawson business would see its sales rise by about £250m over the next 12 months, but warned that the short time frame meant its costs would be higher than usual.