Vela X is a region of extended radio emission in the western part of the Vela constellation: one of the nearest pulsar wind nebulae (PWNe), and associated with the energetic Vela pulsar (PSR B0833-45). Extended very-high-energy (VHE) $\gamma$-ray emission (HESS $\mathrm{J0835\mhyphen 455}$) was discovered using the H.E.S.S. experiment in 2004. The VHE $\gamma$-ray emission was found to be coincident with a region of X-ray emission discovered with ${\it ROSAT}$ above 1.5 keV (the so-called \textit{Vela X cocoon}): a filamentary structure extending southwest from the pulsar to the centre of Vela X. A deeper observation of the entire Vela X nebula region, also including larger offsets from the cocoon, has been performed with H.E.S.S. This re-o...