There is an easy solution to this. Assume you aim for a certain degree of historical accuracy or at least believability. You let your character get captured in Africa, sold to a British slave trader who intends nothing else but fill a ship full of people to be sold in America. All still conforming to the popular school knowledge of triangle trade, the Amistad like ship sets sail in Africa headed West but then has a mishap at sea.
Usually, seaman in distress are rescued if anyone in the vicinity notices what has happened. If the survivors get picked up by another slaver heading in the same direction that might be some tough luck. But there are other examples:
From your desired year, List of shipwrecks in 1770:
Expedition: Great Britain – African slave trade: The ship foundered in the Atlantic Ocean abouth 35 leagues (105 nautical miles (194 km) off the coast of Senegal. Her crew and a passenger were rescued by James ( Great Britain), but not the 110 slaves on board. (Jan, 16)
Expedition: Great Britain – African slave trade: The sloop was discovered at sea crewless by Giegson of the River ( Great Britain). Her 110 slaves were taken on board and Expedition was sunk. She was on a voyage from Senegal to the West Indies. (Unknown date)
Fly: Great Britain – The ship was wrecked on the coast of Gold Coast, Africa. (unknnown date)
These dates are taken from the register of an insurance company. That the Expedition is listed twice with exact numbers of slaves gives any author the perfect excuse to use the other one as reference when accused of inaccuracies.
These incidents were not entirely uncommon. Traders, military ships went all over the place, also directly from Africa to Britain. The higher the urgency of the voyage for the rescuer the less likely it would be to drop any survivors from the wrecked ship off somewhere else. Perishable goods, military matters, your choice.
Whether plot-wise this is a problem or an opportunity, it should be considered that concerning the exact year:
The Somersett Case in 1772, in which a fugitive slave was freed in England with the judgement that slavery did not exist under English common law and was thus prohibited in England, helped launch the British movement to abolish slavery.