In "The Internal Enemy Slavery and War in Virginia, 1772-1832," Alan Taylor very clearly describes the British Government's strategy of liberating enslaved people in the Chesapeake Bay region as a means of weakening the resolve of the local white populace, harming the local economy, recruiting scouts and people who could help lead the British to local leaders for capture, and standing up whole squads of African American troops to fight for the British in that war and other arenas. At that point the British had a carefully crafted rule that any enslaved person who managed to make it to a British ship or fort was deemed free. Many enslaved people evidently stole small boats in the night to effectuate their escape. Slave owners even came to the ships to demand the return of their "property" and the British flat out refused them. In fact, enslaved people frequently led British troops back to the farms where they had been enslaved with the express purpose of liberating the family and friends of the enslaved person who had managed to reach the safety of the British. It appears that the freed slaves were treated very well by the British.

While this does not answer your specific question about freeing all enslaved people, it was clearly a policy in the Chesapeake area to try to free people, and it appears hundreds or perhaps thousands were freed.

FYI, some of the freed slaves descendants still live in Trinidad today and are called "Merikins." In fact a professor from the University of South Carolin, David Shields, has been going there to collect seeds of of crops that they brought with them and which are now extinct here in the continental US.

/u/Machipongo has it right in his answer, down to the book I'd have cited.

One thing: the British empire did not abolish slavery in 1807. They abolished the slave trade, which basically means no more importing people from Africa to British possessions in the western hemisphere but you can keep whoever you own now, buy and sell people, and own any children born to women you own. The United States did the same thing that year, effective 1 January 1808.

Abolition (freeing the slaves) in both jurisdictions didn't come for decades thence. The UK abolished slavery in most of the Western Hemisphere effective 1834, though it carried with it an "apprenticeship" system that would have stretched things out to 1840 or so. That was rescinded in 1838 in favor of full freedom. British possessions elsewhere were not emancipated until the 1840s.

The US came almost dead last among western slaveholding powers and didn't emancipate until the end of 1865.

Sort of related; What were the goals of the British had they 'won' the war of 1812 against the U.S.? Would they have attempted to subjugate America as a British dominion, or would it have been a peace agreement of some sort with concessions to the UK?