England players to wear poppies on black armbands for Scotland clash, says FA
The FA says England players will wear black armbands bearing poppies during their World Cup qualifier against Scotland on Armistice Day
In a statement, the FA maintained the remembrance poppy did not a represent "a political, religious or commercial message".
In a statement the FA said: "The poppy is an important symbol of remembrance and we do not believe it represents a political, religious or commercial message, nor does it relate to any one historical event.
"In keeping with the position agreed with Fifa back in 2011 and in what we believe is in accordance with Law 4, para 4, The FA intend to pay appropriate tribute to those who have made the ultimate sacrifice by having the England team wear black armbands bearing poppies in our fixture on Armistice Day."
That team was allowed to wear the armband poppies in 2011 friendly matches.
The Scottish Football Association says Scotland players will also wear the armbands bearing poppies.
Fifa's laws of the game prohibit commercial, political or religious messages from players' kit, mean poppies cannot be worn.
At Prime Minister's Questions, Mrs May tore into the scandal-hit footballing body as she defended the players' right to wear special kits.
The PM told MPs: "I think the stance that has been taken by Fifa is utterly outrageous.
"Our football players want to recognise and respect those who have given their lives for our safety and security. I think it is absolutely right that they should be able to do so."
She said it was a matter for the English and Scottish Football Associations, but there was a "clear message" from the House of Commons that "we want our players to be able to wear those poppies".
And in a direct message to world football's governing body, which has been plagued by corruption allegations, she said: "Before they start telling us what to do, they jolly well ought to sort their own house out."
A Fifa spokesperson told Press Association Sport: "Fifa fully respects the significance of commemorating Remembrance Day on 11 November each year.
"The laws of the game are overseen by the International Football Association Board and applicable to all 211 member associations. The relevant law four, para four, clearly states that the players equipment should not carry any political, religious or commercial messages.
"The laws are applied uniformly in the event of similar requests by any member association to commemorate similar historical events."
Damian Collins, chairman of the Commons Culture, Media and Sport Committee, said the ban was insulting to British fans.
He told BBC Radio 4's Today programme: "I hope common sense prevails. Fifa has strict rules banning political, religious or commercial symbols from shirts. I think it is insulting to people in this country to say a poppy is one of those sort of symbols.
"Someone has shared with me on social media an Ireland football shirt that has a special embroidery on marking the centenary of the Easter Rising.
"Fifa allow that, so I think people will find it astonishing that the poppy's not allowed."
Former culture, media, and sport secretary John Whittingdale insisted the two home nations should defy Fifa and risk a potential points deduction.
Condemning Fifa's stance, he told BBC Radio 5 Live: "For them to try and brand the poppy as a political symbol shows a total misunderstanding, and I think there are a number of reasons why we are already profoundly unhappy with Fifa's behaviour and conduct and this adds to that list."
Asked if the teams should risk a points loss, Mr Whittingdale replied: "Yes."
Elsewhere, a petition set up by former RAF pilot and prisoner of war John Nichol on change.org, urging Fifa to change its mind, has garnered more than 260,000 signatures.
He wrote: "The poppy is not a political statement at all. It could not be further from a political statement.
"It is a statement of remembrance and an acknowledgement of sacrifice from the First World War right through to the sacrifices of our young men and women today."
Mr Nichol added: "No-one should ever be banned from wearing a poppy and it brings shame on Fifa that they continue to propagate this misunderstanding of our heritage."