With the widespread integration of renewable energy sources and distributed energy storage systems, intraday dispatch of distribution networks (DNs) has gradually evolved into a multistage sequential decision-making problem with intertemporal state coupling and progressively revealed uncertainty. Stochastic optimization under the stagewise independence assumption and limited horizon prediction cannot adequately capture temporal transition characteristics, which may lead to biased future cost estimation and myopic decisions. To address this obstacle, this paper proposes a conditional-cut-enhanced Markov chain stochastic dual dynamic programming strategy (MC-SDDP-CC) for multistage intraday dispatch of DNs. Feature encoding and scenario-lattice-driven trajectory sampling with Markovian path dependence are introduced to accurately characterize the temporal dependence in DNs. To improve computational efficiency, a node-wise conditional cut management scheme is developed to accelerate the recursion and tighten the conditional value function approximation. Numerical studies on modified IEEE 33-bus and 123-bus networks, as well as a practical system in a southwestern province of China, verify the effectiveness of the proposed method in terms of optimality, scalability and ablation performance.