If you have a Wifi connection and it asks you permission to use your current location (may have trouble getting a GPS signal indoors), then yeah it should work.
But as soon as you get out of range of that Wifi connection, you probably need to re-establish your location and whatever you looked up before is probably lost.
Is the London A-Z app. some kind of a travel or city guide with listings of restaurants and so on? Well a lot of free, small apps. need a connection to pull data over the Internet.
There are guides which install all the information to your iPhone, so they will be much bigger, like maybe a couple hundred megabytes. I think there are Frommers apps. for some cities, which are suppose to be like an electronic version of their guide books. Those probably won't need a data connection but you have to pay like $15 up front to buy them.
That's how the GPS turn-by-turn apps like Navigon and Tom Tom work. Instead of streaming the map data over the Internet like the built-in Maps app., these install all the map data on your iPhone, so you don't need an Internet connection of any kind, which makes them useful overseas.
I found some free apps. which save the data locally. But they're in French, like Cityzeum, which I used in Madrid. Honestly, if I had a Wifi connection, I just looked up stuff on my MacBook Pro, which I also had with me.