Are you obliged when attempting to overtake, in this situation, to ensure that you do not get in the way of a vehicle travelling in the right lane?

A driver, when performing an overtaking manoeuvre, is required to exercise particular care and to ensure that they do not impede the movement of other drivers. This obligation applies to all road users in the vehicle's vicinity, including those in the right-hand lane. This is particularly important if a change to the right-hand lane is necessary after completing the manoeuvre.