There was a small community of free Black persons in 18th century London - the exact numbers are hard to come by, because records such as parish burials don't necessarily record race, but the Old Bailey Online project estimates that there were between 5,000 and 10,000 Black people in London by the 1780s. There were far more men than women, primarily down to the fact that most enslaved people who ended up in London before being freed were sailors or manservants to army/naval officers, government officials, merchants and other travelling men.

Assuming you had come to London (and it would probably be London, or another Atlantic port such as Liverpool or Bristol), and were subsequently freed, the chances were that you would remain a servant or sailor, using the skills which you already had in order to make a living. The vast majority of Black Londoners simply became part of the working class community in the city, marrying local women, frequenting taverns and alehouses, and so on. There were several establishments which catered to a predominantly Black clientele, especially in the east of the city along Wapping and Ratcliff, but no evidence of formal segregation.

A small number of freedmen were able to establish themselves in securely middle-class lives, and to participate in the literary and cultural life of London. The 'Sons of Africa' was an informal association of former slaves who had become writers and abolition activists, formed in the 1780s. Its members included Ignatius Sancho, Olaudah Equiano, and Ottobah Cugano - Equiano and Cugano both published abolitionist books, while Sancho was a composer, business owner and 'man of letters' corresponding with notable figures of the day.

It is significant that all of these men were able to access cultural and financial capital through a combination of their own talents, and patronage from white aristocrats and intellectuals. There were many liberal-minded Britons who abhorred slavery and worked to eradicate it; however, there was frequently a streak of paternalism in their interactions with Black people. For example, the author Samuel Johnson, whose personal servant Francis Barber was a freed slave, demonstrated affection and respect for Barber in his letters, but also insisted on sending him to school at the age of around 30, so that Barber might be better equipped to act as the servant of a literary man. Johnson left Barber a legacy of £70 a year in his will - a substantial amount of money, and enough to live on in a small way - which enabled Barber to marry and open a school in Lichfield, Staffordshire.

So the short answer is: your life would probably not change that much in practical terms, but of course you would be liberated from the legal fiction of being another person's 'property'. You might, with patronage and luck, be able to start a business and move in celebrated circles. You would not be able to live a life free from racism and verbal abuse, but you would more or less be able to go about your business unmolested, and become just another Londoner in a city of one million people.