The number issued to people in Northern Ireland also doubled, in the largest monthly increase since the Brexit vote.
June's result has sparked a marked rise in the number of people applying for Irish and European Union passports.
November is normally one of the quietest months of the year for passport applications.
But the total number from Northern Ireland - 4,569 - was up by more than 600 from October.
Some 6,855 people people in Great Britain applied for an Irish passport in November 2016, a significant jump from 3,133 last year.
Applications from Northern Ireland went up from 2,267 in November last year to 4,569 last month.

The Belfast women alleged they were abused over a three-year period in the late 1990s, when they were teenagers.
They claim the case was delayed because prosecutors gave precedence to a separate court case, involving allegations made by MÃ¡iria Cahill.
The PPS said the decision had been made by the court and not them.
The women said they had been "utterly let down by the criminal justice system".
Both women, who have retained their right to anonymity, released a statement through their solicitor, outlining the background to their case and the delays they faced in bringing the matter to court.
The two women said they first reported the alleged abuse to the Police Service of Northern Ireland (PSNI) in January 2010.
They said their case was "constantly adjourned" and then postponed two days before the trial was due to begin.
In November 2012, the women's legal representatives made complaints about the handling of the prosecution case to the Public Prosecution Service (PPS), the Office of Attorney General and the Department of Justice.
The solicitor said that shortly after a meeting with police and prosecutors in December 2012, during which there was a "frank exchange of views", the two women "reluctantly withdrew their statements".
The statement issued on behalf of two women said: "They had lost all faith and trust in the criminal justice system and believed they were being exploited, merely for political point scoring."
The statement also made reference to appointment of Keir Starmer QC to lead an independent review of three prosecution cases linked to Ms Cahill's allegations.
The women questioned the independence of the review and called for clarification on its powers and terms of reference.
Five people accused in connection with the cases linked to Ms Cahill's allegations were all acquitted in court.
A PPS spokesperson said: "The Public Prosecution Service has commissioned an independent review of these interlinked cases.
"It is intended that the review will consider all aspects of the cases, which may be unprecedented in complexity as they involve not only multiple complainants but also serious charges relating to sex abuse offences and terrorist-related offences.
"We can confirm that all of the complainants in the cases have been invited to participate in the process and it is our hope that each of the individuals involved will agree to do so.
"The approach will be robust and rigorous and any lessons to be learned from the cases will be addressed openly and transparently."

Eleven babies and one mother died as a result of maternity failings at Furness General Hospital between 2004 and 2013.
A subsequent inquiry report identified 20 failings linked to the deaths.
Health Secretary Jeremy Hunt told the House of Commons that when things go wrong in the future "they will no longer be swept under the carpet".
The inquiry into the Morecambe Bay NHS Foundation Trust - led by Dr Bill Kirkup - found the maternity unit at Furness General had been "dysfunctional" with "substandard care" provided by staff "deficient in skills and knowledge".
It also found working relationships between doctors and midwives were extremely poor, with midwives referring to themselves as "the musketeers" as they pursued normal childbirth "at any cost".
Accepting the findings of Dr Kirkup's report, Mr Hunt said the Nursing and Midwifery Council (NMC) would no longer be responsible for the statutory supervision of midwives in the UK.
He said a decision had been made to move to a model of professional supervision similar to that of other health professionals.
He also promised a new independent NHS patient safety investigation service would be set up by April 2016.
Mr Hunt said a national review of maternity services would continue to look at how safe care could be delivered in geographically isolated areas.
Welcoming Mr Hunt's comments, a spokesman for the NMC said: "As seen through the tragic events at Morecambe Bay, the current set up is open to conflicts of interest, which in not in the best interests of public protection."
More than twice the number of Irish passports were issued to people in Great Britain last month than in November 2015.
[NEXT_CONCEPT]
Two women who claim they were sexually abused by an alleged IRA man have said they withdrew their statements because of how prosecutors dealt with the case.
[NEXT_CONCEPT]
Changes to the way midwives are supervised have been announced by the government in response to an inquiry into baby and mother deaths in Cumbria.