  We have used narrow emission line data from the new 7C Redshift Survey to
investigate correlations between the narrow-line luminosities and the radio
properties of radio galaxies and steep-spectrum quasars. The 7C Redshift Survey
is a low-frequency (151 MHz) selected sample with a flux-density limit about
25-times fainter than the 3CRR sample. By combining these samples, we can for
the first time distinguish whether the correlations present are controlled by
151 MHz radio luminosity L_151 or redshift z. We find unequivocal evidence that
the dominant effect is a strong positive correlation between narrow line
luminosity L_NLR and L_151, of the form L_NLR proportional to L_151 ^ 0.79 +/-
0.04. Correlations of L_NLR with redshift or radio properties, such as linear
size or 151 MHz (rest-frame) spectral index, are either much weaker or absent.
We use simple assumptions to estimate the total bulk kinetic power Q of the
jets in FRII radio sources, and confirm the underlying proportionality between
jet power and narrow line luminosity first discussed by Rawlings & Saunders
(1991). We make the assumption that the main energy input to the narrow line
region is photoionisation by the quasar accretion disc, and relate Q to the
disc luminosity, Q_phot. We find that 0.05 < Q / Q_phot < 1 so that the jet
power is within about an order of magnitude of the accretion disc luminosity.
The most powerful radio sources are accreting at rates close to the Eddington
limit of supermassive black holes (~ 10^9 - 10^10 solar masses), whilst lower
power sources are accreting at sub-Eddington rates.
