The Computer Misuse Act was introduced in 1990. However, due to the rapid development of internet technology, it was recently updated in 2008. Amongst many things, it criminalising activities such as computer hacking.
The Misuse of Drugs Act was brought in during 1971. It created three classes of controlled drugs; A, B and C. It made it illegal to both supply and possess controlled drugs.
Image on the left - 19th century opium use.
There were (obviously!) no motoring offences before cars were invented. The Motor Car Act, which came into force in 1904, introduced registration of motor cars and licensing of drivers in the UK and increased the speed limit.
Some crimes received much harsher sentences than today. For example, in 1787 the first ship sailed from Portsmouth to Australia transporting many people convicted for crimes such as theft.
The Somersett case in 1772 took place after Charles Stewart, a Customs officer from Massachusetts, brought his slave James Somersett to England. Although the case did not free slaves in Britain, the King's Bench did rule that it was unlawful to forcible remove a person from the country to be soled in to slavery.
Heresy laws punished people for speaking out against the Church. In the reign of Mary Tutor people convicted of heresy were executed, typically by being burnt to death.