Tourism has emerged as one of the leading components of aggregate economic growth in most developed economies, especially in the UK, where it is predicted to grow at an annual rate of 3.8% through 2025. Because tourism demand represents individuals choice between leisure and work, a persistence of negative shocks, such as Brexit uncertainty, can be detrimental to the growth of tourism via its impact on agents utility function of a directed consumption of leisure for a specific country. This note fills a gap in the literature by providing an econometric estimate of time-varying volatility in tourism demand following Brexit-driven Economic Policy Uncertainty. Using seasonally adjusted and trend-extracted tourist arrival series along with Brexit uncertainty, we find a strong evidence of long-run persistence in (asymmetric) volatility in tourist arrival. In particular, the BREXIT referendum appeared to create ambiguity among international visitors to the UK. Our results have important policy implications.