The original London Season was the period when Parliament was in session. ("Sitting" in British usage.)
They and (especially) their wives had to have entertainments. Soon, the entertainments took on a life of their own.
We must remember that in the Regency period, even the House of Commons represented the upper classes. a Member of Parliament -- as such -- drew no salary in the 19th century. So, only those with an independent income would consider this career.
When parliament sat, peers had a reason to be in London; their wives had these entertainments. This concentrated more of the social elite than could be concentrated at any other place and time.
During the Season, the creme of young girls were presented at court. Before they were 16, young women did not mix in society, even when they were in the same house in which their parents were entertaining. Most of them spent the year in the family's country seat.
Then they were brought to London and sent into the center of society.
The richer families could afford to have a daughter attend balls for several seasons; many of the families on the edge of the ton could not. Their daughters were expected to attend one season, get engaged, and wed. Even when the family could afford it, lasting though the season without a proposal was considered a failure.
Arranging marriages in the season wove the upper class together. The bride would often come from a different region of Britain than the groom, and they would return to the groom's home and set up a household there. After a few generations, almost anyone in the elite of any county would have a cousin in the elite of any other county.
Some women who married in the season spent their married lives in one season after another; others did not return until their daughters needed the exposure. Every season was full of these fresh faces. To them and their mothers -- and sometimes their fathers and other relatives -- the chance of proposals was what the season was about.
Meanwhile, London was a huge city and the largest port of the most important maritime nation in the history of the world. Shipping companies, ships' chandlers, importers, exporters, merchants in silk. tea, sugar, cotton, and cod flourished in the streets of London.
Many of the workers were impoverished, but some of the owners could afford luxuries.
Along with the exclusive balls, dinners, luncheons, and teas, London provided dramas, concerts, dramas, and other entertainments that high society shared with not-so-high society. Some of the lordlings enjoyed the amusements patronized by London _hoi polloi_, as well.
Then, too, there were entertainments, like fireworks, for the entire populace.
One reason that those who could choose did not schedule their time in London for the summer was that cities were susceptible to epidemics.