... when the UK is considering an exit from the European Union ...
It is UKIP and the right wing base that is supporting the UK exiting the EU. The Labour Party and the unions oppose leaving the EU largely because of the workers' rights that come with EU membership. I am glad that Obama backed the position favored by British unions.
Blame FDR for modern globalism. He inherited a country that republicans had saddled with high tariffs, restrictive immigration laws and an isolationism that kept the US from joining the League of Nations (which failed) or any other international organization or agreement. There was no hint of globalism under Calvin Coolidge or Herbert Hoover - just nationalism. Sounds a lot like Trump.
FDR created his own (liberal?) new world order which deemphasized nationalism and the nation state in favor of international cooperation and multilateral action on global problems. The UN, the IMF, the World Bank, the International Trade Organization (which republicans killed but from with GATT and the WTO evolved), all came from the mind of FDR, not from Coolidge, Hoover or any other republican. Unsurprisingly given who created them, the modern republican base wants the US to withdraw from the UN, the IMF, the World Bank and the WTO.