The two major forms of revivalism were the Gothic Revival and Neo-Classicism, which became locked in a vigorous debate which is now known as the "Battle of the Styles". Both the Gothic and Classical Revivals were established in the 18th century.
In the Georgian era (1714-1830), architecture was dominated by aristocrats, because by and large only they were educated and could afford to build. It was felt that an aristocrat's education should include a tour of Europe and it became fashionable to take the "Grand Tour" of Italy and Greece. This was a form of cultural tourism. They visited the major cultural sites: the monuments of ancient Greece and Rome, and the cities of the Italian Renaissance.
When they returned to England they built houses based on the styles they'd seen. The Chiswick House in Middlesex (1732) was designed by Lord Burlington [Fig. 1]. He had toured Italy and was inspired by the work of the Italian Renaissance architect Andrea Palladio. So this is an imitation of buildings produced during the Renaissance, the age of Leonardo and Michelangelo.

Fig. 1 Chiswick House, Middlesex
The Palladian style was influential in Britain. This is a Palladian chapel in Gibside, a landscape garden in County Durham [Fig. 2]. Here the form of the Palladian villa has been adapted into a church. This was designed by James Paine.

Fig. 2 Gibside, County Durham
Gibside was one of a number of 18th century pleasure gardens that aristocrats built for themselves. They built lavish country houses that stamped their authority on the landscape, but they also used these spaces to experiment with different styles by building small garden buildings.