On Friday, Twitter user Susan Hindle Barone shared a picture of her new passport side-by-side with her old one.
In response to a tweet from Barone, Catherine Sutherland said: "I don't understand how the Home Office can do this while still in the European Union though".
Mr Brady and his partner Jan both sent off their passport renewal applications on 21 March.
Drivers who held pink plastic permits under European Union standards were told to get ready to apply for worldwide licenses in case Britain left without a deal.
His partner's passport, which was printed on 4 April, features the European Union logo on the front and the inside.
Of course, the blue passport was emblematic of the United Kingdom government's promise to "take back control" after the 2017 election.
Following her appeal, Conservative MP Nigel Evans said on Saturday night that if May failed to deliver Brexit and all she could do was secure a long extension at an European Union summit on April 10, she would face an overwhelming pressure to step down.
"There will be no difference for British citizens whether they are using a passport that includes the words European Union, or a passport that does not".
Both passports remain equally valid for travel, the Home Office said, and a new blue passport design would be rolled out from late 2019.
The former Vote Leave frontman and two-time Mayor of London described Labour's hard-left leader as a "Marxist" who is "not fit to govern", emphasising his continuing support for the "Bolivarian revolutionary socialism" which has reduced oil-rich Venezuela to a state of penury.
In a post on Twitter, she said she was "truly appalled" and "furious", adding any mention of the European Union had been removed from inside the passport too. She had previously tweeted a photo comparing her old and new passports.
In the event that the United Kingdom introduces a visa requirement for nationals of at least one member state in the future, the existing reciprocity mechanism would apply and the three European Union institutions and the member states would undertake to act without delay in applying the mechanism.