We define intrinsic torsion in generalised geometry and use it to introduce a new notion of generalised special holonomy. We then consider generic warped supersymmetric flux compactifications of M theory and Type II of the form ${{\mathbb{R}}}^{D-\mathrm{1,1}}\times M$. Using the language of ${E}_{d(d)}\times {{\mathbb{R}}}^{+}$ generalised geometry, we show that, for $D\geqslant 4$, preserving minimal supersymmetry is equivalent to the manifold M having generalised special holonomy and list the relevant holonomy groups. We conjecture that this result extends to backgrounds preserving any number of supersymmetries. As a prime example, we consider ${ \mathcal N }=1$ in D = 4. The corresponding generalised special holonomy group is ${SU}(7)$, giving the natural M theory extension to the notion of a G 2 manifold, and, for Type II backgrounds, reformulating the pure spinor ${SU}(3)\times {SU}(3)$ conditions as an integrable structure.