Spending several days in a large city, by yourself can be pretty daunting. Luckily, being familiar with the inner workings of a large city (specifically, New York) London was manageable to navigate solo. What really made it possible though, were the following apps:
Known as the busiest airport in the world, London's Heathrow definitely needs a great app to navigate it. Luckily, the official LHR app is just that. I found it to be the most accurate for arrival/departure terminals and gates. There's also maps, restaurants, shopping info and more.
Once you've landed and navigated the elevators and tubes towards your exit, the next order of business will be getting into the city. The best and cheapest option is to take the Heathrow Express train that goes directly from the airport to Paddington Station (you'll feel like you're in a movie). This £20 ride beats the £80-100 (that's close to $150) it takes for a taxi into the city. You can purchase your ticket directly from the app, and the attendant can scan the barcode right from your iPhone's screen.
If you've ever experienced the New York City subway you'll feel right at home. With one of the best public transportation systems in the world, the tube can take you basically anywhere in London. This app (among others I tested) is probably the best. It even allows you to input a starting / ending tube stop and will map out every changeover required, including short walks. This is a must have.
As this was a business trip, I tried my best to keep track of purchases as I made them, rather than being overwhelmed upon my return to the U.S. One receipt doesn't do a great job of scanning and interpreting your receipts, but it's quick and easy enough to manually input the merchant (using Foursquare locations or directly), item and price. Once I returned home, you can login to their website (for free) and download a .CSV file of your purchases. This made my expense report hassle-free.
It probably doesn't even need to be said, but Google Maps was invaluable as I traversed London and the English countryside. Street view, pedestrian directions, points of interest, and even turn-by-turn driving directions later in my trip all worked great. So yes, Google Maps beats Apple Maps both here in the States, and across the pond.
As an honorable mention, Goop City guides includes New York, Los Angeles and London. The app is fueled by personal recommendations (and videos) from actress Gwyneth Paltrow and her online magazine Goop. I didn't get a chance to use it much while in London, but the "POI Near You" maps and numerous suggestions would be very useful if you have some extra time.