We present the results of high-quality pre-refurbishment HST imaging polarimetry of NGC 1068 obtained with the Faint Object Camera in the ultraviolet (lambda similar to 2700-3700 Angstrom), and the Wide Field Planetary Camera in the visual (lambda similar to 5000-6000 Angstrom), with resolutions of 0 ''.06 and 0 ''.08, respectively. The polarization of the UV continuum is very high, peaking at similar to 60% in the vicinity of the emission line knot 4 ''.5 NE of the nucleus. To a high degree of precision the polarization vectors show the centro-symmetric pattern expected from scattering from a point source. By locating the centre of symmetry of this pattern we have determined the location of the hidden nuclear source, to an accuracy of +0 ''.05, which lies 0 ''.6 south of the emission peak. A pair of highly polarized clouds (P similar to 45% in the UV) lies close to the position of the scattered nuclear source. The degree of polarization after correction for dilution is close to 100%, indicating that this is a reflection image. These clouds are associated with the ''twin-crescent'' object, a ringlike or double-jet like feature. Their peculiar properties suggests that they are related to the hidden nucleus. They probably represent reflection clouds produced by an expanding bipolar structure, or a jet. The hidden nucleus would lie at its center. The WF/PC-I polarization images contain contributions from both optical continuum and emission lines. However, these two components are spatially separated The continuum polarization dominates in a quasi-linear region starting at the location of the ''hidden nucleus'' and including the continuum peak, knot B. The nature of this pattern suggest that the nuclear light might be collimated. The large-scale polarization structure is dominated by scattered line emission. The source of this scattered [O III] emission is predominantly the bright observed region of line emission in the NLR, knot B. Therefore, scattering is also very important for narrow lines and this must be taken into account when trying to understand the kinematics and morphology of the NLR. The nuclear radiation cone is only partly filled with scatterers; the minimum angular extent is from PA-15 to PA + 55, corresponding to an opening angle greater than 70 degrees, but it is probably as large as 100 degrees. It is difficult to establish the precise association between radio and optical emission because of the relatives errors between the respective reference frames. Adopting the registration of Evans et al. leads to the conclusion that there is no significant radio emission from the nucleus. This maybe because the radio nucleus is radio quiet, or, as both the theoretical model of the torus and the X-ray data imply, the column density in front of the nucleus is sufficient that free-free absorption obscures it even at centimeter wavelengths. Alternatively, if the flat spectrum southern radio component is assumed to be the nucleus, then there appears to be no direct spatial correspondence between the radio and the emission line structures.