Plan your travel time carefully. London's tourist season is in the spring and summer, so you might be able to find some deals not only on airfare but on hotels as well if you plan on going in the winter. Keep in mind that the weather won't be as nice and many things are closed during the winter months, but if you're planning on spending a few weeks, there will still be plenty to do.
Decide which airport you want to fly into. While Heathrow is much closer to London, and there's an Underground station right at the airport, you'll usually find you pay more to fly into Heathrow than into Gatwick. If you chose the cheaper flight into Gatwick, though, you're going to have to find a way into London. That will mean hiring a cab, taking the train or taking the bus - all while carrying your luggage, mind you. If you're only saving $100 going into Gatwick, you're better off heading for Heathrow.
Decide where to stay. Prices for hotels in London can be expensive and this will be your biggest expense. Keep in mind that you're only going to be in the room while you're sleeping, so you can afford to skimp on it. Hostels are one option, and so are privately owned bed and breakfasts. However, there are some decently priced hotels right in the heart of London, so use your Internet and look for some affordable rates. One of the easiest things to do is get a hotel within walking distance of an Underground station. From there, you can get anywhere, and you'll save on cab and bus fare.
Get an Oyster card. These are pre-paid cards that you can use for the Underground. Scan them as you go through the turnstile, and you're on your way. With Oyster cards, there's no fumbling with schedules and trying to figure out how much you need to buy a ticket. They're refillable at any station, and using them costs less than a cash fare. With the insane cost of gas, this is a much more cost-efficient way to travel through the city than renting a car.
Shop around for a place to get your money changed. Airports give notoriously bad exchange rates, and there are plenty of places throughout London that can do better. Pay attention not just to the exchange rates, but to the percentage a money changer will charge per transaction. The fewer transactions you make, the better, as you'll be charged for each one.
Do your shopping at the grocer's. If you're planning to spend the day at a tourist location, do your shopping first. Grocers are all over London, and if you stop there first to pick up your drinks and snacks for the day, you'll find yourself paying a lot less. A bottle of water that costs $2 American at a grocer will go for $8 American in Hyde Park, so it's worth carrying.
Walk where you can. Taking the Underground is a quick and easy way to get around London, but walking to your destination is a great way not only to see the city but to save some money as well. Make sure you have a good book of maps. You will probably stumble across some hidden jewel that you wouldn't have seen otherwise. Cut through the squares, look at shop windows, walk through any number of parks; it's all free!
Choose your destinations carefully. There are plenty of free things to do in London, and you don't have to look hard to find them. Hyde Park, Covent Garden, Kensington are all free to see. Most cathedrals, churches, and some castles will charge a minimal fee for entrance, while some are more pricey.
Consolidate. Look at your map before you go out. There are often a number of places that are within walking distance of the same tube station. Make these into one day's outings; you'll save on tube fares.
Look for package deals. If you're planning on visiting the Tower of London, Hampton Court, or Kew Palace, you can get a package deal through Historic Royal Palaces, where you'll pay a flat fee that will grant you entrance to a handful of palaces and castles. If you want to see only a couple of them, it will still save you money in the long run.
Watch where you eat. Most restaurants will have menus posted outside so you can check out the food and the prices before you set foot inside. If they seem a little pricey, keep walking; there will be another restaurant just down the street.
Check around for ticket prices if you're planning on going to the theatre. Sometimes you can find good deals in advance, but the best bet is ticket kiosks that will sell drastically discounted tickets on the day of or day before the show.