We report on an optical (SDSS) and X-ray (XMM) study of an optically selected sample of four dual AGN systems at projected separations of 30--60~kpc. All sources are detected in the X-ray band (0.3-10 keV); seven objects are optically identified as Seyfert, while one source, optically classified as a LINER, is likely powered by accretion in virtue of its relatively high X-ray luminosity (1.2$\times10^{41}$ erg/s). Six of the eight objects are obscured in X-rays with N$_{\rm H} \geq$ 10$^{23}$ cm$^{-2}$; three of these, whose X-ray spectrum is dominated by a reflection component, are likely Compton-thick (N$_{\rm H} \geq$ 10$^{24}$ cm$^{-2}$). This finding is in agreement with the hypothesis that galaxy encounters are effective in driving gas inflow toward the nuclear region, thus increasing the obscuration. We compare the absorption properties in our dual AGN with those in larger samples observed in X-rays but selected in different ways (optical, IR and hard X-rays). We find that the obscured (N$_{\rm H} \geq$ 10$^{22}$ cm$^{-2}$) AGN fraction within the larger sample is 84$\pm$4 per cent (taking into account the 90 per cent error on the N$_{\rm H}$ measure) up to large pair separations ($\sim$100~kpc). This is statistically higher than the fraction of obscured AGN in isolated galaxies found in X-ray surveys.

18 pages, 7 figures. Accepted for publication in MNRAS