Since Britain accounts for a major share of the world's wine imports, and EU member countries include the world's major wine exporters, Brexit and subsequent UK and EU-27 bilateral free-trade agreements (FTAs) have the potential to disrupt wine markets globally. We use a model of the world's national wine markets, projected to 2025, to examine potential impacts of Brexit and a series of follow-on bilateral FTAs. The scenarios assume a UK-EU-27 FTA is followed by EU-27 bilateral FTAs with Australia and New Zealand and then UK bilateral FTAs with those two plus South Africa and Chile (with whom the EU already has FTAs). The new EU-Japan FTA is also assessed. Brexit's impact comes more from assumed changes to the UK's income growth and the pound's exchange rate than to its tariffs. The bilateral trade consequences of the trade-diverting and trade-creating effects of each additional FTA are highlighted. They are then compared with the effects of a multilateral agreement to remove all wine import tariffs globally. Unrealistic though this is, it exposes the far bigger benefits to wine producers and consumers that could emerge from a single multilateral undertaking than from several bilateral or regional FTAs.