We have investigated the redshift space distortions in the optically selected Durham/UKST Galaxy Redshift Survey using the 2-point galaxy correlation function perpendicular and parallel to the observer ’ s line of sight , \xi ( \sigma, \pi ) . We present results for the real space 2-point correlation function , \xi ( r ) , by inverting the optimally estimated projected correlation function , which is obtained by integration of \xi ( \sigma, \pi ) , and find good agreement with other real space estimates . On small , non-linear scales we observe an elongation of the constant \xi ( \sigma, \pi ) contours in the line of sight direction . This is due to the galaxy velocity dispersion and is the common “ Finger of God ” effect seen in redshift surveys . Our result for the one-dimensional pairwise rms velocity dispersion is < w ^ { 2 } > ^ { 1 / 2 } = 416 \pm 36 kms ^ { -1 } which is consistent with those from recent redshift surveys and canonical values , but inconsistent with SCDM or LCDM models . On larger , linear scales we observe a compression of the \xi ( \sigma, \pi ) contours in the line of sight direction . This is due to the infall of galaxies into overdense regions and the Durham/UKST data favours a value of ( \Omega ^ { 0.6 } / b ) \sim 0.5 , where \Omega is the mean mass density of the Universe and b is the linear bias factor which relates the galaxy and mass distributions . Comparison with other optical estimates yield consistent results , with the conclusion that the data does not favour an unbiased critical-density universe .