One user shared a picture of their new passport complete with the words European Union at the top.
At present, Britain's exit date is April 12, although European Union member states are mulling a new extension request by British Prime Minister Theresa May.
However, it said some newly-issued travel documents would still bear the bloc's name - which has sat atop British passport covers - in a bid to save public money.
Britain was due to leave the European Union on March 29 and the HM Passport office began printing new covers this week when it didn't think the departure would be delayed. March 30 was the original date set by the enacting of Article 50 for the exit of Britain from the European Union.
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Brexit Secretary Stephen Barclay said Wednesday that May was entering her talks with Corbyn "without preconditions". Could Britain leave the European Union without agreements, that would be the responsibility of the United Kingdom.
What British passports will look like post-Brexit has been a sticking point and a rallying call for some, after a decision by the United Kingdom government in 2017 to change passports from burgundy to dark blue.
The Home Office said the removal of the words "European Union" was part of a two-stage redesign process.
In an apt sign of the befuddling circumstances around Brexit, Britain's interior ministry confirmed that some newly-issued passports now omit references to the European Union atop the cover while others still bear the bloc's name.
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Experts have warned for years that the Parliament building, one of London's most famous landmarks, needs urgent repairs. If the bill passes into law, May will have to go to a special EU Brexit summit in Brussels on April 10 to seek a delay.
But the other 27 members must give unanimous backing to any further postponement and are increasingly impatient at the paralysis in Westminster. "Both designs will be equally valid for travel", she said.
The Home Office have said that the old versions will still be sent out until stocks run out "in order to achieve best value to the taxpayer".
British passports had already become ensnared in the country's Brexit divisions after the government announced in 2017 it would return to traditional blue passports "to restore national identity".
The new production contract is to begin in October 2019, with the passports now being issued without reference to the European Union on them still in the burgundy colour.
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By the end of the year, the burgundy passports are scheduled to be replaced with the dark blue design British passports had before the European Union came about.