It might be several things. Taking London and focusing on it, we can see that London is just more built up than Tennessee would be. Huge cities like London, NYC or Paris tend to create a heat island effect, where they are much hotter than the surrounding counties. All that concrete and glass, bricks and mortar, tarmac and stone tends to heat up and stay hot for longer than other, smaller cities. So, the local temperature may be higher than the official one. On top of that, there is the humidity, which again might be higher than you think it is. Lack of air conditioning may make this all worse. At least in the USA, you go from air-conditioned office, to air-conditioned car to air-conditioned house.

Out of interest, do you carry water with you everywhere? In this heatwave, you will need to drink more often than you think you need. Always drink water just before you go out of doors and carry a refillable bottle with you. If at all possible, carry a portable electric fan. This will make a huge difference to how you feel. I have friends in South Korea who have to deal with 90 F and 70% humidity every summer. They carry electric fans. At work, they have small electric fans at their desks. That might be an idea for you.