alternatehistory.com

(Sources: "A Short History of Canada", Desmond Morton (2017); "The Penguin History of Canada", Robert Bothwell (2007))

The period after the war saw diverse patterns of development throughout British North America; Upper Canada had suffered most from the War and its effects crippled the economy for years; the other colonies had profited greatly during the war but would see asymmetric development as the British demand for Canadian timber grew, and the old farmlands of the east grew depleted with population growth.
The existing Mercantile system gave the colonies special economic benefits (in the form of favourable duties and a protected market), and local politicians were generally preoccupied with economic development. These factors contributed to the growing numbers of immigrants.

America was in an aggressive and expansive mood at this time, and the Spanish colonies were convulsed in revolution. Relations were by no means easy, but American policy slowly drifted its attention away from the British colonies in the years after the war.

The steam engine would be applied in lumber mills and factories, and eventually to railways, transforming the traditional agricultural and fur trading economies. The timber trade led to the settlement of the Ottawa and Miramichi valleys.
The decline of the fur trade precipitated the merger of the Hudsons Bay and Northwest companies in 1821; but the Montréal merchant elite easily transformed into bankers and manufacturers. Their prosperity led to the creation of the Bank of Montréal in 1817 and McGill University in 1821. The city grew in wealth and population and became the dominant financial, commercial and distribution centre of the Saint Lawrence basin.
Montreal's prosperity contrasted with economic stagnation the rest of Lower Canada, where population pressure erased the huge agricultural surpluses posted at the turn of the century. A generation later, and the Canadiens were finally leaving the Saint Lawrence valley in large numbers, to establish farms on more marginal (but virgin) land further west and north.
The worsening economic conditions contributed to a radicalization of the populace; who began to echo the sentiments growing in other colonies for responsible government.

Of course, the "other colonies" were independent of Lower Canada, with governors taking orders directly from Britain, and so "British North America" existed in theory only at this time.

In Nova Scotia, Halifax was the largest town, colonial capital and home to a University, a Royal Navy base, an army garrison and an Anglican bishop. However, with is impeccable English/Loyalist character, it was seen as remote and aloof from its hinterlands - which in the southwest was populated still largely by Acadien farmers and fishermen, and in the northeast by the descendants of highland Scots, many Gaelic speaking and few Anglican.
In 1835, journalist Joseph Howe began a tirade against the corrupt appointed Colonial council; he would be elected to the Assembly in 1836 and wasted no time in writing a letter to the colonial authorities demanding disestablishment of the Anglican Church and responsible government.

Upper Canada had been devastated by the conflict, and remained a backwater, lacking sufficient roads, bridges, or population. Its decision to no longer allow "Late Loyalist" immigration from America sent a flood of qualified frontiersmen south to Ohio and upstate New York, while overpaid officials, vast tracts of valuable land held for clergy and crown, all contributed to economic distress. It would be debt financing of canal construction which would bring the immigrants necessary to see economic growth.
However, the common pioneering and defensive experiences had helped to alleviate some of the social tensions that previously existed between different groups. Given the valour of Upper Canada's black community during the War, another 4,000 "Black Refugees" (who had escaped slavery to help the British during the assault on Washington, DC) were allowed to settle as Loyalists around London in the Huron tract.
Given that the vast majority of migrants to Upper Canada during this time were not Anglican, they began to echo the sentiments of the other colonies.

-Gzowski, "Our Cultural Mosaic"