Both the Chelsea Football Club and the Arsenal Football Club are popular in London. Arsenal does have more league championships compared to Chelsea, so you could argue that they are more popular. There is more to popularity than simply winning championships however. Fans connect with the players and the identity of the team, not necessarily the championships.
In my opinion Arsenal is still a more popular football club in London than Chelsea but this is not necessarily because of the championships. They are also active in the community, donate to the Great Ormond Street Hospital Children's Charity and Save the Children.