The British really didn't have any plans for future colonization. When the American Revolution began Britain was attempting to stabilize its current colonies to make them profitable. The Proclamation of 1763 forbid the American colonists to expand into the areas gained during the Seven Years War. This was for two reasons first it was difficult to control or tax people spread over so large a region and second colonial expansion was causing trouble with the native tribes who lived in those territories.

Certainly Britain was interested in taking as much land as possible but the Seven Years War had caused Britain to be deeply in debt. More land meant more problems. To secure larger areas of land Britain would have to increase the size of its military. Deeply in debt Britain could scarcely afford to do this. Plus the American Colonies weren't producing the mountains of gold the British had hoped for.

If you recall the Hessians of the American Revolution that was the British attempt to build an army quickly and cheaply. Why did they need a quick cheap army? They had spent years reducing the size of their military trying to keep costs down. When the American Revolution broke out the British Army wasn't ready to fight a war.

The British hoped by restricting migration they could increase the population of already existing colonies especially in the American South. By 1775 The French colony of Saint-Domingue (now the Dominican Republic more or less) was producing more money for France than all of Britains colonies combined produced for Britain. The British wanted to copy this success.

Unfortunately a successful plantation colony needed workers. What kind of workers? Britain preferred colonists. Slaves were expensive. Settlers in the colonies were actually much cheaper and mostly took care of themselves. Not only that but settlers paid taxes and taxes paid for government.

Basically Britain wouldn't turn down a valuable colony if they could acquire it but when the American Revolution broke out Britain was trying to build the colonies it already had into profitability. Sometime in the future they had plans to settle the areas east of the Mississippi they had acquired in the Seven Years War.

Around 1750, Britain was effectively hemmed in - there was nowhere to go, and as a consequence, not much of a colonization policy outside the existing colonial territories.

The British were active around Hudson's Bay in a fur-trading capacity, but that was pretty inhospitable land, and colonization was not feasible in the 1700s.

The 7 Years War changed all that around 1763, with Quebec and northern New France switching to British control, and linking the colonies with the Hudson's Bay Company lands. But with the war debt and the small amount of time between the end of that war and the start of the Revolution, there was not enough time to bring about a change in colonization policy.

After the Revolution, colonization did resume, but on quite different terms. British North America spread right to the West Coast. This latter colonial policy was in many respects a reaction to American settlement policy - if the British did not actively colonize the west, American settlers would eventually simply occupy the lands and the question of governance would become moot. This actually happened in the Oregon Country, which was originally occupied by British traders, but was eventually overwhelmed by American settlers, starting in the 1830s.

The British ceded control up to the 49th parallel in the Oregon Treaty of 1846, but then actively colonized the lands north of there to prevent a replay - forming the colonies of Vancouver Island (1849) and British Columbia (1858). 50 years of subsequent colonial policy then sought to join these west coast colonies with those in the east, beginning with the establishment of the Dominion of Canada (1867), adding the west coast colonies to it in 1871, and then gradually filling in the gap with a string of self-governed provinces.