We present a 30h integration Very Large Telescope X-shooter spectrum of the Lyman series forest towards the $z = 7.084$ quasar ULAS J1120+0641. The only detected transmission at ${\rm S/N}>5$ is confined to seven narrow spikes in the Ly$α$ forest, over the redshift range $5.858 5.5$. The data nevertheless provide only a weak limit on the volume-weighted hydrogen intergalactic (IGM) neutral fraction at $z∼ 6.5$, $x_{{\rm HI}} > 10^{-4}$, similar to limits at redshift $z∼6$ from less distant quasars. The new observations cannot extend measurements of the neutral fraction of the IGM to higher values because absorption in the Ly$α$ forest is already saturated near $z∼6$. For higher neutral fractions, other methods such as measuring the red damping wing of the IGM will be required. ; Comment: Accepted for publication in A&A. 11 pages, 10 figures