We report on measurements of the cosmological constant , \Lambda , and the redshift space distortion parameter \beta = \Omega _ { m } ^ { 0.6 } / b , based on an analysis of the QSO power spectrum parallel and perpendicular to the observer ’ s line of sight , P ^ { S } ( k _ { \parallel } , \mathbf { k } _ { \perp } ) , from the final catalogue of the 2dF QSO Redshift Survey . We derive a joint \Lambda - \beta constraint from the geometric and redshift-space distortions in the power spectrum . By combining this result with a second constraint based on mass clustering evolution , we break this degeneracy and obtain strong constraints on both parameters . Assuming a flat ( \Omega _ { m } + \Omega _ { \Lambda } = 1 ) cosmology and a \Lambda cosmology r ( z ) function to convert from redshift into comoving distance , we find best fit values of \Omega _ { \Lambda } = 0.71 ^ { +0.09 } _ { -0.17 } and \beta _ { q } ( z \sim 1.4 ) = 0.45 ^ { +0.09 } _ { -0.11 } . Assuming instead an EdS cosmology r ( z ) we find that the best fit model obtained , with \Omega _ { \Lambda } = 0.64 ^ { +0.11 } _ { -0.16 } and \beta _ { q } ( z \sim 1.4 ) = 0.40 ^ { +0.09 } _ { -0.09 } , is consistent with the \Lambda r ( z ) results , and inconsistent with a \Omega _ { \Lambda } = 0 flat cosmology at over 95 per cent confidence .