This study uses the Bayesian approach of Wang (1998) to examine the impact of no short selling constraints on the mean-variance inefficiency of linear factor models in UK stock returns and to conduct model comparison tests between the models. No short selling constraints lead to a substantial reduction in the mean-variance inefficiency of all factor models and eliminate the mean-variance inefficiency of some factor models in states when the lagged one-month UK Treasury Bill return is higher than normal. In model comparison tests, the best performing model is a variant of the Fama and French (2018) model with a momentum factor and using the small ends of the value, profitability, investment, and momentum factors.