We present radial velocity measurements of a sample of M5V -M9V stars from our Red-Optical Planet Survey, ROPS, operating at 0.652 -1.025 µm. Radial velocities for 15 stars, with r.m.s. precision down to 2.5 ms −1 over a week long time scale are achieved using Thorium-Argon reference spectra. We are sensitive to planets with m p sin i 1.5 M ⊕ (3 M ⊕ at 2-σ) in the classical habitable zone and our observations currently rule out planets with m p sin i > 0.5 M J at 0.03 AU for all our targets. A total of 9 of the 15 targets exhibit r.m.s. < 16 ms −1 , which enables us to rule out the presence of planets with m p sin i > 10 M ⊕ in 0.03 AU orbits.Since the mean rotation velocity is of order 8 kms −1 for an M6V star and 15 kms −1 by M9V, we avoid observing only slow rotators that would introduce a bias towards low axial inclination (i ≪ 90 • ) systems, which are unfavourable for planet detection. Our targets with the highest v sin i values exhibit radial velocities significantly above the photon-noise limited precision, even after accounting for v sin i. We have therefore monitored stellar activity via chromospheric emission from the Hα and Ca II infrared triplet lines. A clear trend of log 10 (L Hα / L bol ) with radial velocity r.m.s. is seen, implying that significant starspot activity is responsible for the observed radial velocity precision floor. The implication that most late M dwarfs are significantly spotted, and hence exhibit time varying line distortions, indicates that observations to detect orbiting planets need strategies to reliably mitigate against the effects of activity induced radial velocity variations.