The desire for further expansion is often brought up, but there's little period sources to support that. The British did put a bar on further expansion of the colonies (out of fear of antagonizing other European powers with the Seven Years war so recent - they didn't give the slightest trace of a shit about the natives), but it was pretty obvious that wasn't going to last forever.
But the royal proclamation was to avoid antagonising the natives further, not the French, who already had ceded their interests in NA. The British were keen to maintain their commercial and military alliances with those tribes who had them; and those who did not, were not by any means defenceless, but rather were the foremost military threat to an expensive western colonial frontier. It's only after native tribes could no longer buy guns from the French to use against the British and guns from the British to use against the French that their military potential greatly dwindles in the face of post-colonial states; many forts were overrun for this exact reason, and defending a large expanse of forest by turning your allies into enemies would be impractical and expensive in the extreme.
It was their strategy to balance the power of the French colonists, American colonists and native tribes[/url]
Likewise, the fairly common claim that the American Revolution was to save slavery is baseless. In 1775, there was only a small abolition movement, and it was very weak.
It's unfair to say they fought to save slavery, but slavery was definitely an issue which the crown ministers could easily exploit, e.g. criticising fighting for liberty whilst carrying a whip, recruiting a large loyalist population from slaves by promising freedom for service, and in the UK the anti-slavery movement was well established amongst an influential minority of members of parliament, royal navy captains and judges - and as a result of the 1772 ruling that slavery had no basis in English common law (in two years later in Scottish), British colonials were divided between those supportive of the new wave of abolitionism or who supported a clean break from English common law to protect themselves from the ruling
That's internal debate, which isn't what I was talking about. There is (or was, I haven't seen it in a little while) a loud revisionist argument that Britain was all set to ban the "peculiar institution" and that's the real reason the colonies rebelled. Despite the fact that Britain wouldn't ban slavery itself until the 1830s, and that was probably because they lost the colonies (when the sugar islands collapsed, the pro-slavery side lost just about all funding, which wouldn't have happened with the planters of Virginia still in play) as much as anything else.
It is a peculiar revisionism, as it was just one reason that some pro-slavery individuals held, but not one held by all, nor the main one. Although a quick correction - Britain banned slavery in the entire Empire in the 1830s; it was illegal in Britain from 1772, the trade itself made illegal in 1807; Wellington pushed for an anti-slavery clause in the congress of Vienna after receiving hundreds of thousands of signatures in petitions against slavery, and RN Captains caused diplomatic incidents by attacking allied and neutral country slaverships on their own initiative because they figured whilst on the Atlantic ocean no one in Westminster could stop them, let alone reach them for contact. It is a feature, not a bug that the UK law changes with the policy, not the policy to change to the law