A lot depends on your definition of 'culture'. There's the culture of the arts, and music for example, or there's the people. London as a city and not just a tourist destination, now actually has a bigger population from other cultures and ethnicity than indigenous British people. As such it makes it that much more difficult to mix culturally in that way. If your idea of tourist attractions is the usual hot ten, then I'd say just go off with your cousin and explore, rather than sign up for the usual stuff. And, when it's safe to do so, try to strike up some conversations with other people. You can do that fairly safely in cafes, pubs, (which you should definitely be visiting), and sometimes even on the underground (The Tube), or on buses. But be careful and aware of your safety, and don't be put off if not everyone wants to engage with you. Go to areas with atmosphere like Covent Garden and enjoy the market, and the cafe culture where opera singers may suddenly burst into song (for a small donation), and there are many good places to enjoy food or a drink. When visiting tourist areas, don't take a taxi or pile onto a soulless bus provided by your hotel, but take, for example, a trip down the Thames to see something like the Tower of London, or plan your route on The Tube. Camden is also a great market to visit, and for antiques and collectibles with atmosphere, try Portobello Road. Hope you have a great trip!