  Suppose that a group $G$ has socle $L$ a simple large-rank classical group.
Suppose furthermore that $G$ acts transitively on the set of lines of a linear
space $\mathcal{S}$. We prove that, provided $L$ has dimension at least 25,
then $G$ acts transitively on the set of flags of $\mathcal{S}$ and hence the
action is known. For particular families of classical groups our results hold
for dimension smaller than 25.
  The group theoretic methods used to prove the result (described in Section 3)
are robust and general and are likely to have wider application in the study of
almost simple groups acting on finite linear spaces.
