 By May 2020 Montgomerie had become a frequent critic of the government, in particular of the Prime Minister's Senior Adviser Dominic Cummings and the Prime Minister himself.In 2019, Montgomerie was reported as saying that the British government should have a "special relationship" with Hungary post-Brexit, saying at a meeting of the Danube Institute that “Budapest and Hungary have been home, I think, for an awful lot of interesting early thinking on the limits of liberalism, and I think we are seeing that in the UK as well.So I hope there will be a special relationship with Hungary amongst other states.”

Montgomerie is a Christian.