In 1426, Scotland decided to follow the Danes & Dutch on their trips, established colonies around Cape Cod, which was called New Scotland ITTL. But as soon as 1463/64, England defeated Scotland and took their colony, which was renamed New England, of course. The capital of the colony, Perth beyond the Ocean, was renamed after the winner of the battle, Boston. England slowly extended its settlements, until they went from OTL Bar Harbor, Maine, to New Haven, Connecticut. But now they found that the Danish colonies along St Lawrence river together with Prince-Harald-Island and Anderland formed a belt around the English colonies.
After some clashes with Danish colonists in Atlantis, the Quadruple Monarchy declared the anti-Danish War against Denmark 1509. The Dutch allied with them. In the peace of Hamburg in 1512, Denmark lost its lands in Canada to the Quadruple Monarchy and Anderland to the Netherlands. Only the city of Haraldsborg (OTL New York, plus Long Island) and Prince-Haralds-Land (Newfoundland, as a base for fishermen) stayed in their hands. (And the former went to New England after the English-Polish War for a short time too.)
When the Triple Monarchy of England-Castille-Portugal broke apart in the Old World in 1628, most of the colonies declared their loyalty to Spain (OK, former Castille, right). Only a few islands in the Caribbean and the northern colonies in OTL Canada and New England stayed loyal to king Henry VI. But when the king was deposed and England fell into Civil War, in 1637 the Dissenter's Revolt took place in New England. Denmark-Braunschweig, supported by France, used the situation to expand there / take old lands back. Only Markland (Canadian Maritimes and OTL Quebec) could defend itself during this decades, ironically, thanks to its strong garrison. Denmark-Braunschweig got Haraldsborg back, plus became protector of the Commonwealth of New England (the dissenters preferred "the papist German king in Europe to the papist English governor in Markland"). German immigration now also went to New England, where many new settlements were founded. English loyalists emigrated to Markland.
Under Danish-German rule
Since 1650, the settlements in the colonies of Denmark-Braunschweig (and also Florence), plus the New English Commonwealth, meanwhile had reached the official border to the French-claimed territory, which was still mostly settled by native Atlanteans.
After having accepted the loyalty of Markland, king Humphrey I planned to regain England's old colony in North Atlantis. However, the states of Denmark-Braunschweig and Florence allied and fought 1652-56 against him in the "Atlantean Coalition" and surprisingly defeated the English fleet. New England stayed a Danish-German protectorate.
1671, said Protectorate of New England was split up into three countries: One containing the Boston-RI area, one with upper Massachusetts, Connecticut and the south of NH and VT, and one with most of VT and NH, south of Maine.
From then on, a slow but steady demographical change began. The language border between English and (Lower) German slowly went north; first in Boston and the other big cities, later in the smaller ones too, the population was germanized from the top, when the administration, the merchants and eventually the whole middle class started speaking German, to communicate with Martinsburg and Haraldsborg; English-speaking settlers left for the west, or Canada, and were replaced by Germans. (The name Neuengland stuck however.) Still, it would take until the Technocracy to make German mandatory in schools, and even at the present (1993) you can find old natives in little villages with English as first language.
1794, Britain tried to take advantage of Denmark's fall and retake the latter's part of Atlantis, at least New England, but in vain. Shortly after, the Schulzenaufstand gave German Atlantis independence; and although there were still people in New England who wanted to join Canada, or at least preserve the English language, but the federal nature of the lands allowed such pecularities to survive without getting a majority.