The burgundy passports were introduced from March 30, the day after Britain was expected to leave the EU.
Some passports including the words European Union will continue to be issued while the remaining stock is used up, the Press Association reports.
But those applying for a new travel document will not be able to choose between the two.
Susan Hindle Barone, who picked up her new passport on Friday, said on Twitter she was “truly appalled”.
“I was just surprised – we’re still members of the EU,” she told the Press Association. “I was surprised they’ve made the change when we haven’t left, and it’s a tangible mark of something which I believe to be completely futile.
“What do we gain by leaving? There’s certainly a whole lot we lose. Let’s face it, it’s not the changes to the passport – it’s just symbolic.
“What really matters are the potential changes to our country – the damage to the economy, our communities and our international standing.”
Reaction to the tweet was split, inevitably between Leavers and Remainers.
The decision to remove the words was made in anticipation of Britain leaving the EU at the end of last month.
Dark blue passports are scheduled to be issued from the end of this year.
A Home Office spokeswoman said: “Burgundy passports that no longer include the words European Union on the front cover were introduced from 30 March 2019.
“In order to use leftover stock and achieve best value to the taxpayer, passports that include the words European Union will continue to be issued for a short period after this date.
“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 designs will be equally valid for travel.”