Offord supported Brexit in the 2016 UK EU membership referendum. He is a member of the European Research Group. Offord voted for then Prime Minister Theresa May's Brexit withdrawal agreement in March 2019. He also voted against any referendum on a Brexit withdrawal agreement in the indicative votes on 27 March. He supported Boris Johnson's bid to become Conservative Party leader in 2019, and after he became prime minister voted for his Brexit withdrawal agreement in October.