  We prove existence, uniqueness and Sobolev regularity of weak solution of the
Cauchy problem of the stochastic transport equation with drift in a large class
of singular vector fields containing, in particular, the $L^d$ class, the weak
$L^d$ class, as well as some vector fields that are not even in $L_{\rm
loc}^{2+\varepsilon}$ for any $\varepsilon>0$.
