By slavery I am assuming you're mainly wanting to know about slavery in the 17th to 19th century.

However, slavery in Britain pre-dates that by a long way. We see slavery exist in Britain from before even the Romans came here, whilst we don't know a huge amount of this, we do know that by 1066 roughly 10% of England's population were slaves. We can tell this from the Doomsday Book.

Despite this, after the Norman conquest of England, slavery largely disappears, replaced by a feudal society, and in specific serfdom.

Laws on villeinage never made abolished it outright, it still existed into the 17th century, however it did make it pretty obsolete.

Okay, now I'm getting to your proposed timeline. Slavery, or forced labour was used as a punishment for criminals and the like from 1597, under the English Vagabonds Act. Under this, the monarch could transport criminals to forced labour areas, however this was rarely used, despite James I pushing it in 1615, 1619 and 1620. It was only after the Irish uprising and subsequent putting down by Cromwell that it became popular, many Act for the Settlement of Ireland in 1652 was used to transport some Irish families as indentured servants overseas, at this point mainly to North America.

However, due to industrialisation we can see forced labour become popular domestically in Britain between the 17th to 19th century with the setting up of poorhouses. Whilst poorhouses wasn't slavery, it was a choice between working for a pittance and starving. Many were forced into poorhouses instead of being homeless.

Slaves as in blacks from North Africa though were rare, whilst Britain was one of the biggest slave traders, very few slaves ever saw Britain, those that did were usually household servants.

Slavery was abolished in 1807 (Slave Trade Act) in the UK, and forced labour as a punishment was abolished in 1997 (Human Rights Act). However the number of actual slaves in the way of American slavery was incredibly low in the UK, this is mainly due to need.

American slavery was used to work in massive plantations, and the fact that the native population wasn't really that useful for the work (in the way India was) meant that slaves brought in from other countries was much easier. In the UK we see no need for slaves, whilst there were farms, we already had lots of need for those agricultural jobs Britain didn't need anything else. Therefore the only slaves in Britain tended to be household slaves. Indentured Servants or forced labour in industrial work however was popular, especially poorhouses being used as a way to "help" the poor was used, and often used child labour until 1833 and 1844 we see child labour laws.

Sources

Seaton, A. V. (2001). Sources of slavery-destinations of slavery: The silences and disclosures of slavery heritage in the UK and US. International journal of hospitality & tourism administration, 2(3-4), 107-129.

Beech, John G. (2001) The Marketing of Slavery Heritage in the United Kingdom. International journal of hospitality & tourism administration, 2(3-4)

Doomsday Book