My question is simple. Where do the Deathly Hallows originate from, Britain or somewhere else. Also when and how did the Hallows (more specifically the Elder Wand) find their way outside Britain?
The Elder Wand most likely originated in Britain.
The Elder Wand was likely created by one or more of the Peverell brothers. Ignotus Peverell, the third brother, was born in Godric's Hollow.
“The Cloak, as you know now, travelled down through the ages, father to son, mother to daughter, right down to Ignotus’s last living descendant, who was born, as Ignotus was, in the village of Godric’s Hollow.” - Harry Potter and the Deathly Hallows, Chapter 35 (King's Cross)
He was also buried in Godric's Hollow. So, he at least, is confirmed to have both been born and died in Britain. It is possible that the Peverell brothers left Britain at some point in their lives, but this at least implies that they might have been created in Britain (since the Peverell brothers were almost certainly the creators of the Deathly Hallows).
“Who are the Peverells?’ asked Ron.
‘That was the name on the grave with the mark on it, in Godric’s Hollow,’ said Hermione, still watching Xenophilius. ‘Ignotus Peverell.” - Harry Potter and the Deathly Hallows, Chapter 21 (The Tale of the Three Brothers)
From after Emeric the Evil had it, it isn't said where any of its owners were located until Gregorovitch. The only time that one of the Hallows is confirmed to have left Britain is when Gregorovitch had it, though it could have left Britain before that. It's unclear whether he took it out of Britain himself, or someone else did and he got it from then. Both Gregorovitch and Grindelwald were confirmed to have the Elder Wand outside of Britain, then the Elder Wand returned to Britain when Dumbledore won it from Grindelwald.
The Elder Wand's Suspected Owners Through History
The Peverell brothers - owners and likely creators of the Elder Wand
Located in Britain
Emeric 'the Evil'
Located in England
“The first well-documented mention of a wand made of elder that had particularly strong and dangerous powers was owned by Emeric, commonly called “the Evil,” a short-lived but exceptionally aggressive wizard who terrorized the south of England in the early Middle Ages. He died as he had lived, in a ferocious duel with a wizard known as Egbert.” -The Tales of Beedle the Bard
“What became of Egbert is unknown, although the life expectancy of medieval duelers was generally short. In the days before there was a Ministry of Magic to regulate the use of Dark Magic, dueling was usually fatal.” -The Tales of Beedle the Bard
(The whereabouts of the Elder Wand is unknown for a century.)
“A full century later, another unpleasant character, this time named Godelot, advanced the study of Dark Magic by writing a collection of dangerous spells with the help of a wand he described in his notebook as “my moste wicked and subtle friend, with bodie of ellhorn,25 who knowes ways of magick moste evile.” (Magick Moste Evile became the title of Godelot’s masterwork.)” -The Tales of Beedle the Bard
“Godelot is known to have perished in his own cellar, where he was locked by his mad son, Hereward. We must assume that Hereward took his father’s wand, or the latter would have been able to escape, but what Hereward did with the wand after that we cannot be sure.” -The Tales of Beedle the Bard
(The whereabouts of the Elder Wand is unknown until the early eighteenth century.)
“All that is certain is that a wand called the “Eldrun27 Wand” by its owner, Barnabas Deverill, appeared in the early eighteenth century, and that Deverill used it to carve himself out a reputation as a fearsome warlock, until his reign of terror was ended by the equally notorious Loxias, who took the wand, rechristened it the “Deathstick,” and used it to lay waste to anyone who displeased him. It is difficult to trace the subsequent history of Loxias’s wand, as many claimed to have finished him off, including his own mother.” -The Tales of Beedle the Bard
(The whereabouts of the Elder Wand is unknown until Gregorovitch.)
Located - Eastern Europe
Gregorovitch is the wizard known to have taken the Elder Wand to Eastern Europe. He had it and was supposedly studying it until Grindelwald stole it.
“It was a rumour,’ whispered Ollivander. ‘A rumour, years and years ago, long before you were born! I believe Gregorovitch himself started it. You can see how good it would be for business: that he was studying, and duplicating, the qualities of the Elder Wand!” - Harry Potter and the Deathly Hallows, Chapter 25 (Shell Cottage)
Located - all over Eastern Europe
“Gregorovitch had the Elder Wand, a long time ago,’ he said. ‘I saw You-Know-Who trying to find him. When he tracked him down, he found that Gregorovitch didn’t have it any more: it was stolen from him by Grindelwald. How Grindelwald found out that Gregorovitch had it, I don’t know – but if Gregorovitch was stupid enough to spread the rumour, it can’t have been that difficult.’
Voldemort was at the gates of Hogwarts; Harry could see him standing there, and see, too, the lamp bobbing in the pre-dawn, coming closer and closer.
‘And Grindelwald used the Elder Wand to become powerful. And at the height of his power, when Dumbledore knew he was the only one who could stop him, he duelled Grindelwald, and beat him, and he took the Elder Wand.” - Harry Potter and the Deathly Hallows, Chapter 25 (Shell Cottage)
In the chapter "King's Cross" in Book 7, Dumbledore tells Harry that the brothers more than likely did not actually meet Death and receive the hallows but were very clever and invented them:
"I think it more likely the Peverell brothers were simply gifted, dangerous wizards who succeeded in creating those powerful objects."
As to being in Britain, it can be assumed the brothers lived in England because of their family plot being in Godric's Hollow:
"He [Grindlewald] wanted to come to Godric's Hollow...because of the grave of Ignotus Peverell. He wanted to explore the place the third brother had died."
The wand moved across Europe because it was stolen frequently, and most notably by Grindlewald.