One of the unintended consequences of Brexit, the UK’s exit from the European Union, is that it exposes Israel to new pressures as Britain drops out of European engagement and decision-making.After Germany, the UK has been one of the strongest supporters of Israel in all the interlocking institutions of the EU.Although criticisms – many justified – have been raised against EU funding for some Palestinian outfits, especially those doing so-called educational or cultural work, it has suited both Washington and Jerusalem to let the EU pay the lion’s share of international financial support for the Palestinian Authority to try and keep at bay Hamas and Hezbollah.But if the UK – the second biggest net contributor to the EU budget after Germany – pulls out of the EU, the finance chiefs in Brussels will be looking at where to cut outgoings, and support for nonviolent development in the Middle East can easily fall victim.Successive British prime ministers from Margaret Thatcher to Gordon Brown have been both philosemites and strong supporters of Israel. David Cameron made a stupid remark about “Gaza being a prison camp” but that was due to ignorance about Hamas, about which he appeared to have known as little as he did about the forces at play in Britain that would produce the Brexit vote.Britain’s Catherine Ashton, the first EU commissioner for foreign affairs, 2009-2014, is married to Peter Kellner, the son of a Jewish refugee from Austria, and was sensitive to Israel’s needs.Theresa May was 58 before she first visited Israel but has been robust in condemning antisemitism and taking action like banning the odious French anti-Jewish “comedian” Dieudonné M’bala M’bala from entering Britain.But if the UK does fully leave the EU it will have to negotiate a trade agreement with Israel to cover the $3 billion worth of imports and exports that go between the two countries. Other EU nations like the Netherlands and Germany do more business with Israel, but British-Israeli trade links are strong and stable.The one cloud on the horizon is the strongly entrenched Boycott, Divestment and Sanctions (BDS) movement in British civil society. BDS activists are well placed in universities and make life a misery for academics who want to do joint research work with Israeli universities and research institutions.The new hard-left Labour leadership denies it is antisemitic but there is no doubting its hostility to Israel and its preference for Islamist ideological politics linked especially to Hamas and to other anti-Israeli groups.The steady growth of British Muslim political activists who are now much greater numerically in left-wing politics than Jewish Labour Party and trade union members and elected officials tends to a sympathetic hearing for any and all aspects of Palestinian internationalism and a knee-jerk condemnation of Israel and Jews in Britain who support the existence of Israel.Brexit allows anti-Israel politics to get a new hearing. There are different stages to Brexit. There is political Brexit, the formal withdrawal of the UK as a member state of the EU. The negotiations on this begin next spring, to be concluded two years later just before the elections to the European Parliament, when no British candidates will offer themselves.Once no more UK politicians, ministers, diplomats take part in EU debates and decisions, Israel will lose friends in key places in Brussels.After the political Brexit, there is the question of an economic Brexit. A full, hardline Brexit means leaving the EU single market and leaving the EU customs union. At the moment every Israeli firm, bank, or fund based in London has what’s called an EU “passport,” which means they can do business anywhere in 27 other nations and a market of 500 million middle class consumers.If Britain quits the single market, at a stroke Israeli businesses will be limited to doing business in the UK only. If Britain leaves the EU customs union it means that every good, or component, coming into England for onward sale to Europe will require customs clearance.Outside the EU single market, Britain will have to negotiate new trade agreements with every other country unless it wants to trade only under World Trade Organization rules, which do not cover services and offer no advantage that bilateral trade deals, at least in theory, should achieve.When it comes to negotiating a UK-Israel trade deal outside the EU framework it will be easy for BDS supporters to insist that the UK demand a ban on any product which the BDS lobby says is made with Palestinian labor or which has links to military and defense work, drones or cyber security.The UK government can resist such linkage but a post-Brexit trade agreement with Israel will be a golden opportunity for the BDS activists to lobby MPs, fill comment pages with anti-Israel articles, and use social media to promote their line.Israel – thankfully – played no part in the Brexit campaign. And Israel has friends in both the pro- and anti-EU camps. But political Brexit means Israel loses a valuable friend in European politics. And if that if followed by full-on economic Brexit – quitting the single market and EU customs union, any subsequent UK-Israel trade deal will be seized by the BDS campaigners and all who dislike Israel to try and score points.The author is the UK’s former minister of Europe, who coined the term “Brexit” in the Yorkshire Post in January 2012. In January 2015 he published Brexit: How Britain Will Leave Europe (IB Tauris). As a Labour MP he chaired the All-Party Commons Committee on Inquiry into Antisemitism. He is speaking on Brexit at Tel Aviv University on November 17.