We present a study of the radio properties of 870 \mu m-selected submillimetre galaxies ( SMGs ) , observed at high resolution with ALMA in the Extended Chandra Deep Field South . From our initial sample of 76 ALMA SMGs , we detect 52 SMGs at > 3 \sigma significance in VLA 1400 MHz imaging , of which 35 are also detected at > 3 \sigma in new 610 MHz GMRT imaging . Within this sample of radio-detected SMGs , we measure a median radio spectral index \alpha _ { 610 } ^ { 1400 } = -0.79 \pm 0.06 , ( with inter-quartile range \alpha = [ -1.16 , -0.56 ] ) and investigate the far-infrared/radio correlation via the parameter q _ { IR } , the logarithmic ratio of the rest-frame 8–1000 \mu m flux and monochromatic radio flux . Our median q _ { IR } = 2.56 \pm 0.05 ( inter-quartile range q _ { IR } = [ 2.42 , 2.78 ] ) is higher than that typically seen in single-dish 870 \mu m-selected sources ( q _ { IR } \sim 2.4 ) , which may reflect the fact that our ALMA-based study is not biased to radio-bright counterparts , as previous samples were . Finally , we search for evidence that q _ { IR } and \alpha evolve with age in a co-dependent manner , as predicted by starburst models : the data populate the predicted region of parameter space , with the stellar mass tending to increase along tracks of q _ { IR } versus \alpha in the direction expected , providing the first observational evidence in support of these models .