Aims: Already from the initial discoveries of extrasolar planets it was apparent that their population and environments are far more diverse than initially postulated. Discovering circumbinary (CB) planets will have many implications, and in this context it will again substantially diversify the environments that produce and sustain planets. We search for transiting CB planets around eclipsing binaries (EBs). Methods: CB-BLS is a recently-introduced algorithm for the detection of transiting CB planets around EBs. We describe progress in search sensitivity, generality and capability of CB-BLS, and detection tests of CB-BLS on simulated data. We also describe an analytical approach for the determination of CB-BLS detection limits, and a method for the correct detrending of intrinsically-variable stars. Results: We present some blind-tests with simulated planets injected to real CoRoT data. The presented upgrades to CB-BLS allowed it to detect all the blind tests successfully, and these detections were in line with the detection limits analysis. We also correctly detrend bright eclipsing binaries from observations by the TrES planet search, and present some of the first results of applying CB-BLS to multiple real light curves from a wide-field survey. Conclusions: CB-BLS is now mature enough for its application to real data, and the presented processing scheme will serve as the template for our future applications of CB-BLS to data from wide-field surveys such as CoRoT. Being able to put constraints even on non-detection will help to determine the correct frequency of CB planets, contributing to the understanding of planet formation in general. Still, searching for transiting CB planets is still a learning experience, similarly to the state of transiting planets around single stars only a few years ago. The recent rapid progress in this front, coupled with the exquisite quality of space-based photometry, allows to realistically expect that if transiting CB planets exist - then they will soon be found. Based on observations obtained with CoRoT, a space project operated by the French Space Agency, CNES, with participation of the Science Programme of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany and Spain.