As of my last knowledge, there are currently 6 Premier League teams based in London. These teams are:
Arsenal: Based in North London, Arsenal Football Club is one of the most well-known and successful clubs in English football history.
Chelsea: Located in West London, Chelsea Football Club has also achieved significant success in both domestic and international competitions.
Crystal Palace: Situated in South London, Crystal Palace Football Club has a history of competing in the Premier League.
Tottenham Hotspur: Also located in North London, Tottenham Hotspur Football Club is another prominent team in the Premier League.
West Ham United: Located in East London, West Ham United Football Club has a strong following and competes in the Premier League.
Fulham (as of the 2020-2021 season): Fulham Football Club, located in West London, was in the Premier League for the 2020-2021 season. However, please note that team promotions and relegations can change the composition of Premier League teams from season to season.
Please verify this information with more current sources as team promotions and relegations can alter the number of Premier League teams based in London.