This paper presents modelling and control of medium voltage (MV) grid connected modular multi-level converter (MMC) and dual active bridge (DAB) based isolated electrical vehicle charger. The presented model consists of a half bridge sub module (SM) based MMC as first stage and a DAB as second stage of the charger. Firstly, the equivalent model of MMC and DAB is introduced and then a proper control system is designed for both the converters. For MMC level shifted pulse width modulation (PWM) along with shorting algorithm based capacitor voltage balancing technique is used. Two separate voltage and current control loops are designed for DAB. Charging of battery is carried out in constant current (CC) mode upto 80% of its state of charge (SoC) and in constant voltage (CV) mode after 80% SoC of battery. A proper switching mechanism is introduced to minimise the transients during switch-over of DAB controllers. A 3.3 kV, 200 kVA grid connected MMC with a DAB and a 200 Ah, 700 V Li-ion battery system is simulated. Simulation results in steady state and also during controller switch-over process is presented to verify the charging system.