An integrated system of a linear accelerator and a magnetic resonance imaging (MRI) device may provide real-time imaging during radiotherapy treatments. This work investigated changes affecting the dose deposition caused by a magnetic field (B-field) transverse to the beam direction by means of Monte Carlo simulations. Two different phantoms were used: A water phantom (Ph1) and a water-air phantom (Ph2) with a 4-2-4 cm water-air-water cross section. Dose depositions were scored for B-field values of 0 T, 0.35 T, 0.5 T, 1.5 T, 3 T and 5 T. Beams were based on a precalculated photon spectrum taken from an earlier simulated Elekta 6 MV FFF accelerator. All lateral profiles in Ph1 showed a Lorentz force driven shift w.r.t. the B-field strength, presenting a steeper penumbra in the shift's direction. Depositions were shifted up to 0.3 cm for 5 T, showing a constant central axis plateau-dose or an increase by 2.3 % for small fields. Depth-dose curves in Ph1 showed a shift of the dose maximum towards the beam entrance direction for increasing B-field of up to 1.1 cm; the maximum dose was increased by 6.9 %. In Ph2, an asymmetric dose increase by up to 36.9 % was observed for 1.5 T at the water-air boundary, resulting from the electron return effect (ERE). In our scenario, B-field dependent dose shifts and local build-ups were observed, which consequently affect the resulting dose distribution and need to be considered in magnetic resonance guided radiotherapy treatment planning.