Aims: During its flight phase, from 2007-2012, the CoRoT mission delivered light curves for over 2000 eclipsing binaries. Data from the Kepler mission have proven the existence of several transiting circumbinary planets. While light curves from CoRoT typically have lower precision and shorter coverage, the number of CoRoT targets is similar to that of Kepler and some of the known circumbinary planets could potentially be detected in CoRoT data as well. The aim of this work was to reanalyse the entire CoRoT Data set to search for the presence of circumbinary planets and to derive limits on the abundances of such planets. Methods: We developed a code that removes the signatures of eclipsing binaries from the light curves, and searches for quasi-periodic, transit-like features in the light curves after removal of binary eclipses and instrumental features. The code requires little information on sample systems and can also be used for other space missions, such as Kepler, K2, TESS, and PLATO. The code is broad in the requirements leading to detections, but was tuned to deliver an amount of detections that are manageable in a subsequent, mainly visual, assessment of their origin. Results: We identified three planet candidates in the CoRoT sample whose transits would have arisen from a single pass across the central binary; however, no candidates with transit events from multiple planetary orbits remained. We calculated the upper limits for the number of Jupiter, Saturn-, and Neptune-sized planets in co-planar orbits for different orbital period ranges. We found that there are much fewer giant planets in short periodic orbits around close binary systems than around single stars. Full Table 1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/602/A117