Here's a few suggestions to make your first journey to London stress free. Take an orientation tour. Get your bearings by taking an orientation tour, such as those offered on the red double-decker buses. Take the tour on the very first afternoon, or the next morning at the latest. Don't even think about renting a car within the city.
Streets are typically congested, drivers are aggressive and parking is nearly nonexistent.
Not to mention you'd be driving in the left lane. For convenience, purchase a subway pass, which allows speedy entrance and exit of the subway. Buying individual tickets will slow you down and cost more over the long run. Study a city map and subway map before leaving home. You need not be an expert, just get a feel for the place to lessen confusion.