London was voted #3 in last year's trip advisor city guide and it is the fourth most popular city to visit on earth. London is known for its rich heritage, royal buildings, city parks and of of course, that big clock. It is one of the most multicultural cities in the world with over 40% of its population from outside of London. It is also the greenest capital city with over 1000 parks in the city and a huge push for green energy. Its museums also take the top spots globally and it has some of the most famous art galleries too. London's true downfall, is its cost. It is according to last years report in the telegraph the number one most expensive city in the world.
There is some good news. Most of London's main attractions are free (although you should donate if you like them) and the most popular are all within walking distance. On top of that, a recent scheme dubbed 'Boris bikes' allows you to rent a bike and ride on London's delightfully terrifying roads.
I used to try and avoid London altogether, but after moving to the south coast, London is the main link between where I live and where I usually want to be (up North). In the last few months, I've been to London over 20 times and each time, I've been trying my best to not completely blow my wallet away. Here are some of the cheaper things that you can do in London that are equally if not more enjoyable than some of the expensive tourist traps.
Do you need to use the tube? Really, do you need too. It will cost you an arm and a leg but it will save you time. If you only have a very limited time, the tube is usually the quickest way. If you ever have to leave zones, take the bus.
Get an oyster card. Use it on the bus and save a bit of doh and do not forget to cash it in after your trip. You can do this at any underground station but only during working hours.
Don't eat out in Westminster. I know a lot of what you want to see is in Westminster, but do you want to spend your life savings on a shit sandwich? Go over to the Victoria area if you want reasonably priced food. There is a nice fast food place upstairs in Victoria that has helped me survive a few times. It has a McDonalds, burrito place, cafe and sushi stores.
Check Londonist for free events. There is always something going on that will interest you. www.londonist.com
Take free a free tour around the national gallery. Everyday at 11.30 am and 2.30 pm and additional tours on weekends at 4pm.
Check out other free things to do. http://www.visitlondon.com/tag/free-attractions
Stay in a hotel outside of London. There are a few towns on the outskirts of town that can save you serious buck on the accommodation side of things. The most common are Watford junction, Hounslow, Dartford and a few others that you will see when you search for hotels. Consider the price of transport into central London (which can be over 8 pound per person if you travel through enough zones) and if you've had no luck try airbnb.
Try a Boris bike. If you are planning on getting a lot done in a wider area than you'd like to walk, consider hiring a bike for the day. Make sure you be careful though, London is one of the most dangerous cities in Europe for cyclists.
Try a local market. If you do have the opportunity to get out of the main tourist attractions, try and get food from one of London's many markets. Camden market is a great place to get clothes and music stuff and Shoreditch is a rising force in hipster areas. If you do end up on brick lane, try some curry. It's Britain's favorite food and we even have a few of our own curry fusions. Some popular markets are Borough Market (Weds–Sat), Portobello Road Market (Mon-Sat) and the Real Food Market on Southbank (Fri-Sun).
Best city views. If you can afford the price of a cocktail, you can try your luck at Gong on the 52nd floor or Aqua Shard on the 31st floor of the Shard at London Bridge.
Cheapest way to see London by river. Take a commuter train, the best one being the Thames Clipper river boat service from the London eye to Greenwich. If you use your oyster card on this service you can also receive a 10% discount!
Book everything is advance. If you really have to waste half an hour of your life just to say, "I've been on the London eye", at least save a bit of cash doing so. Pretty much all of the main attractions are cheaper online including London zoo, London dungeons and if you are a student you can also make huge saving with your Nus card.
I think that should be enough info for you to save enough to survive. Naturally, you're going to spend more money here than in other cities, but just double check you are getting a good deal.
Have fun!