In this paper, we study the cross-market effects of Brexit on the stock and bond markets of nine major countries in the world. By incorporating information theory, we introduce the time-varying impact weights based on symbolic transfer entropy to improve the traditional GARCH model. The empirical results show that under the influence of Brexit, flight-to-quality not only commonly occurs between the stocks and bonds of each country but also simultaneously occurs among different countries. We also find that the accuracy of the time-varying symbolic transfer entropy GARCH model proposed in this paper has been improved compared to the traditional GARCH model, which indicates that it has a certain practical application value.