Assessment of mental workload is crucial in safety-critical applications. Often, such applications require the user to be ambulant, such as first responders (e.g., paramedics, firefighters, or police officers). Typically, mental workload models have relied on electroencephalography (EEG) signals. EEGs, however, are known to be highly sensitive to movement artefacts, thus limited applications exist for ambulant users and studies have mostly occurred in controlled laboratory settings. In this paper, we explore the robustness of new non-linear features against movement artefacts and test their effectiveness in monitoring mental workload for ambulant users with the end goal of developing mitigation measures based on mental state of operators. To this end, an EEG experiment was conducted where mental workload and physical activity levels were modulated simultaneously and data was collected from 48 participants. Classical EEG features used for workload assessment, such as spectral power and amplitude/phase coherence, were used as benchmarks and compared against the proposed non-linear multi-scale permutation entropy features. Experimental results show the proposed features consistently outperforming the benchmark ones, thus high-lighting their robustness to movement artefacts.