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The cool white dwarf WD 1856+534 was found to be transited by a Jupiter-sizedobject with a mass at or below 14 M$_{\rm{Jup}}$. We used the GTC telescope toobtain and analyse photometry and low resolution spectroscopy of six transitsof WD 1856+534 b, with the intention to derive the slope of the transmissionspectrum, towards an eventual detection of Rayleigh scattering of the particlesin its atmosphere. Such a slope, assuming a cloud-free atmosphere dominated byRayleigh scattering, could be translated into an estimation of the mass of WD1856+534 b. However, the resultant transmission spectrum is essentially flat,and therefore permits only the determination of lower mass limits of 2.4M$_{\rm{Jup}}$ at the 2-$\sigma$ level, or 1.6 M$_{\rm{Jup}}$ at 3-$\sigma$.These limits have implications for some of the proposed formation scenarios forthe object. We elaborate on the potential effects of clouds and hazes in ourestimations, based on previous studies of Jupiter and Titan. In addition, wedetected an H$\alpha$ absorption feature in the combined spectrum of the hostwhite dwarf, that leads to the assignation of a DA classification and allowsderivation of an independent set of atmospheric parameters. Furthermore, theepochs of five transits were measured with sub-second precision, whichdemonstrates that additional objects more massive than $\approx$5M$_{\rm{Jup}}$ and with periods longer than $O(100)$ days could be detectedthrough the light travel time effect

A transmission spectrum of the planet candidate WD 1856+534 b and a lower limit to its mass