It doesn't say anything about the officer being on duty at the time. Besides it would only cover crown servants in the course of the execution of their duty. For example, an armed officer randomly selecting a tourist at the end of Downing Street and putting a few rounds of 9mm into their skull will certainly not be getting away with it.
edit: you may also be interested in knowing where police get the legal right to break the speed limit, which is also obviously not from their non-existent immunity to the law:
> The Road Traffic Regulation Act 1984 and The Traffic Signs Regulations and General Directions 2016 exempt emergency vehicles from:
- observing speed limits
- observing keep left/right signs
- complying with traffic lights (including pedestrian controlled crossings).