The cointegration methodology commonly used for testing the efficiency of the foreign exchange market is applied to a sample of UK share prices. Specifically we test for static market efficiency in the share prices of small and large firms, using monthly data from January 1975 to December 1989. The empirical findings provide evidence of market efficiency for portfolios of large firms but of inefficiency for small firm portfolios. These results are indicative of a small firm effect in the UK stock market.