We present high-quality CCD photometry in the Washington system C and T1 passbands down to T1 ~ 19.5 mag in the fields of 10 Galactic open clusters (OCs) or candidates projected close to the Galactic plane, namely: ESO 313-SC03, BH 54, Ruprecht 87, ESO 129-SC32, BH 217, Collinder 347, Basel 5, Ruprecht 144, Archinal 1 and Berkeley 82. Four of these objects are located toward the Galactic centre direction within a solid angle of 21 deg. No photoelectric or CCD photometry in the optical domain has been so far reported for five of these objects. Cluster radii are estimated from radial density profiles (RDPs) in the cluster fields. Using the cluster Washington (C-T1,T1) colour-magnitude diagrams (CMDs), statistically cleaned from field star contamination, we estimate reddening, heliocentric distance and age of the clusters by fitting Padova theoretical isochrones computed for the Washington system. In all cases, the best fittings were obtained with nearly solar metal content isochrones. Both RDPs and CMDs show that we are dealing with real OCs, except for Ruprecht 87 and Archinal,1 that are found to be probably not physical systems. Differential reddening appears to be present across the fields of ESO313-SC03, ESO129-SC32, BH 217, Collinder 347 and Basel 5. The studied OCs are located at d = 1.0-5.0 kpc from the Sun and at Galactocentric distances R_GC = 6.0-10.6 kpc, with mean reddening E(B-V) in the range 0.10-1.30 mag and ages between 5 Myr (Collinder 347) and ~ 1000 Myr (Basel 5). The estimated linear cluster radii are in the range of 0.4-3.2 pc. In general terms, the results obtained show fairly good agreement with previous photometric results. In some clusters, however, considerable differences are found between the present results and previous ones determined using near-infrared photometric data. The current study provides new OC parameters and some revisions to the OC catalogues.