We examine the rest-frame far-infrared emission from powerful radio sources with 1.4-GHz luminosity densities of 25 ≤ log(L1.4/W Hz−1) ≤ 26.5 in the extragalactic Spitzer First Look Survey field. We combine Herschel/SPIRE flux densities with Spitzer/Infrared Array Camera and Multiband Imaging Photometer for Spitzer infrared data to obtain total (m) infrared luminosities for these radio sources. We separate our sources into a moderate, 0.4 < z < 0.9, and a high, 1.2 < z < 3.0, redshift sub-sample and we use Spitzer observations of a z < 0.1 3CRR sample as a local comparison. By comparison to numbers from the Square Kilometre Array (SKA) Simulated Skies, we find that our moderate-redshift sample is complete and our high-redshift sample is 14 per cent complete. We constrain the ranges of mean star formation rates (SFRs) to be 3.4–4.2, 18–41 and 80–581 M⊙ yr−1 for the local, moderate- and high-redshift samples, respectively. Hence, we observe an increase in the mean SFR with increasing redshift which we can parametrize as ∼(1 + z)Q, where Q = 4.2 ± 0.8. However, we observe no trends of mean SFR with radio luminosity within the moderate- or high-redshift bins. We estimate that radio-loud active galactic nuclei (AGN) in the high-redshift sample contribute 0.1–0.5 per cent to the total SFR density at that epoch. Hence, if all luminous starbursts host radio-loud AGN we infer a radio-loud phase duty cycle of 0.001–0.005.