We present simultaneous photometric and spectroscopic observations of seven young and highly variable M dwarfs in star-forming regions in Orion, conducted in four observing nights with FOcal Reducer and low dispersion Spectrograph2 at European Southern Observatory/VLT. All seven targets show significant photometric variability in the I band, with amplitudes between 0.1-0.8 mag, The spectra, however, remain remarkably constant, with spectral type changes less than 0.5 subtypes. Thus, the brightness changes are not caused by veiling that 'fills in' absorption features. Three objects in the sigma Ori cluster (age similar to 3 Myr) exhibit strong Ha emission and Ha variability, in addition to the continuum variations. Their behaviour is mostly consistent with the presence of spots with temperature of similar to 300 K above the photosphere and filling factors between 0.2-0.4, in contrast to typical hotspots observed in more massive stars. The remaining targets near epsilon Ori, likely to be older, show eclipse-like light curves, no significant Ha activity and are better represented by variable extinction due to circumstellar material. Interestingly, two of them show no evidence of infrared excess emission. Our study shows that high-amplitude variability in young very low mass stars can be caused by different phenomena than in more massive T Tauri stars and can persist when the disc has disappeared and accretion has ceased.