Moody supported the remain campaign in the
2016 EU membership referendum, and supported a delay before
invoking Article 50 to allow for negotiations post-referendum. She supported Britain staying in the
European single market and the
Customs Union post-
Brexit. She chaired the
Labour Movement for Europe from 2017 to 2019, and campaigned for
a second referendum on the final Brexit deal. In 2018, Moody argued that the EU and UK defence and security relationship should remain close despite
Brexit, and that closer
European Union–NATO relations would assist in that and reduce wasteful duplication of effort. In 2023,
The New European reported that she acknowledged Britain would not rejoin in the next parliament, but believed rejoining "will become a question again. For a growth agenda, we have to fix our relationship with the EU." Moody supported
Yvette Cooper in the
2015 Labour Party leadership election. During the leadership challenge to
Jeremy Corbyn in
June 2016, she supported calls for his resignation. ==Personal life==