We present pulsar timing solutions for 374 pulsars. Each ephemeris was obtained by analysing archival data stored at Jodrell Bank Observatory. This data archive contains over 5600 yr of pulsar rotational history with individual data‐spans of up to 34 yr. A new method has been developed to mitigate the effects of timing noise by whitening the pulsar timing residuals. This whitening is applied before standard fitting procedures are followed to measure the astrometric and dispersion measure (DM) parameters of a pulsar. We show that the values obtained using this new technique are consistent with other methods, and that the new timing solutions are, in general, significantly more precise than those in earlier publications. We consider the second derivative of the frequency ν of pulsars, , and the DM gradient, d(DM)/dt, in detail. The values are obtained by fitting to timing residuals that have not been whitened and are found to be orders of magnitude larger than those expected from magnetic dipole radiation; the measured values are dominated by the effects of timing noise, and therefore lead to braking indices that are not consistent with magnetic dipole radiation. We find a dependence between |d(DM)/dt| and DM of pc yr⁻¹, which allows DM variations to be estimated for any radio pulsar.