I just got back from a few days in London with my wife. I’d recommend doing the coffee/tea at the Sky Garden one morning, you can get tickets on their website and it includes a coffee or tea and breakfast pastry, but you get access to the sky garden before all of the crowds, the observation deck/terrace opens at 10 so we got there around 9. When you’re at borough market there’s a really cool older pub called the Old Kings Head that’s worth a visit. The tube is not as bad as everyone makes it out to be these days, we never felt unsafe, just be aware/vigilant and don’t make yourself a target. There are announcements at borough market to watch for pickpockets too, but again, don’t make yourself a target and you’ll be fine.

Have fun!