Context. The extended environment of galaxies contains a wealth of information about the formation and life cycle of galaxies which are regulated by accretion and feedback processes. Observations of neutral hydrogen are routinely used to image the high brightness disks of galaxies and to study their kinematics. Deeper observations will give more insight into the distribution of diffuse gas in the extended halo of the galaxies and the inter-galactic medium, where numerical simulations predict a cosmic web of extended structures and gaseous filaments.Aims. To observe the extended environment of galaxies, column density sensitivities have to be achieved that probe the regime of Lyman limit systems. HI observations are typically limited to a brightness sensitivity of N-HI similar to 10(19) cm(-2), but this must be improved upon by similar to 2 orders of magnitude.Methods. In this paper we present the interferometric data of the Westerbork Virgo HI Filament Survey (WVFS) - the total power product of this survey has been published in an earlier paper. By observing at extreme hour angles, a filled aperture is simulated of 300 x 25 m in size, that has the typical collecting power and sensitivity of a single dish telescope, but the well defined bandpass characteristics of an interferometer. With the very good surface brightness sensitivity of the data, we hope to make new HI detections of diffuse systems with moderate angular resolution.Results. The survey maps 135 degrees in Right Ascension between 8 and 17 h and 11 degrees in Declination between -1 and 10 degrees, including the galaxy filament connecting the Local Group with the Virgo Cluster. Only positive declinations could be completely processed and analysed due to projection effects. A typical flux sensitivity of 6 mJy beam(-1) over 16 km s(-1) is achieved, that corresponds to a brightness sensitivity of N-HI similar to 10(18) cm(-2). An unbiased search has been done with a high significance threshold as well a search with a lower significance limit but requiring an optical counterpart. In total, 199 objects have been detected, of which 17 are new HI detections.Conclusions. By observing at extreme hour angles with the WSRT, a filled aperture can be simulated in projection, with a very good brightness sensitivity, comparable to that of a single dish telescope. Despite some technical challenges, the data provide valuable constraints on faint, circum-galactic HI features.