No? Britain didn't have slavery, it didn't have it before that 1833 Act, and it still didn't have it afterward. The Act's title begins: "An Act for the Abolition of Slavery throughout the British Colonies" because it's about abolishing slavery in the colonies. By this time of course Americans - who still want slavery - have successfully rebelled and are independent and so this law does not affect the millions of slaves in the United States of America.

The Colonies weren't Britain. Their people weren't (on the whole) British citizens, if you knew a bit more history that year might stand out more. 1833 is just after Great Reform, the country has become more small-D democratic, expanding the franchise (the right to vote) to more men and eliminating "Rotten boroughs" which were often in practice controlled by rich people, including slaveowner colonists abroad.