Steps
Consider a walk down the South Bank. The north side of the Thames is where the power (Parliament) and money (the City) historically lived. The South Bank was, until comparatively recently, outside the purview of the London police. It has always been more anarchic than the north side as a result. A glance at historical maps shows that this was the site of the original Globe (and its modern reconstruction), bear pits, taverns, flesh pots and so on. It's a lot more salubrious these days but retains its bohemian heritage as it is home to the Tate Modern Gallery, the Royal Festival Hall, The national Film Theatre, County Hall (home of the now defuct GLC), the Globe and the nice but crowded Borough Market (my local!). A wander along the South Bank is definitely worth it.
Get culture. All the major museums and art galleries are free to enter, but they do solicit donations in order to try to keep them that way. Give what you can. This helps to make London one of the most culturally democratic cities in the world. One highlight is Holbein's "The Ambassadors" in the National Gallery, but with four major galleries and countless smaller ones there is something for everyone. The Big Three museums are in Kensington: the Natural History Museum, the Victoria and Albert and the Science Museum. Each one of these could easily take up to a day to explore, depending on your level of interest, so glance at the websites first if opossible and plan your visit if time is tight. The British Museum is near Euston, on the north side of the city centre. It is large and proverbially quite eclectic (in Artificial Intellignce circles the British Museum search is one which tries each and every path and has no information to help it navigate - you may feel this way after a while in there.)
Walk, don't tube. This is a note for visitors to our fair city: In Zone one in particular, many of the tube stations are quite close together. The tube map is schematic - that is, the distance between stations is not to scale. This makes for a wonderful piece of draughtsmanship but doesn't tell you how far you're travelling. You can get an "Overground/Underground" map in some vending machines on some tube platforms (mainly the ones at mainline stations). These are great for showing alternate walking routes. Or better still, invest in the Londoner's choice: the A-Z. The more dog eared and scribbled on the better! If your feet really are giving out, try the buses. With an Oyster card, fares are very cheap indeed and you get to see the sights. Taking one of the routes that crosses any of the bridges is great fun - especially on the top deck of a double decker. Try the 188, 168 or 68 from Russell Square (by the British Museum) to Waterloo (handy for the South Bank), for a great view from Waterloo Bridge. It's not free, but it's 80p with an Oyster at the time of writing!
Take Your Sandwiches to the Parks. You can walk from Westminster to Knightsbrige almost entirely on grass, thanks to the swathe of parks that cover a large section of central London. These are a restful haven from the rest of the busy, often commercial, city. There are plenty of things to see and do - see the Royal Parks website for maps and guides. Speaker's corner in Hyde Park is particularly entertaining, and will banish forever your view of London as a reserved city. In the north of the city, near Euston, you can find Regent's park - small but very nice, with a well laid out English garden.
Listen and Learn. London is home to a number of institutions: the Royal Society (of science), the Royal Society of Art, the Dana Centre. Quite often these hold free talks by distinguished and/or entertaining speakers. See websites of the respective institutions for details.
Go to a BBC filming/recording. Many BBC radio and TV programs need a live audience. Search the BBC website for audience tickets and fill in the order form. Tickets are free and cover everything from Top of the Pops to Gardners' Question Time.
Catch some free music. The Royal Festival Hall often has music in their foyer - see their website for details. Many churches also have chamber music or choral events that may not be free but that are accessible for a charitable donation.
Find a nearby book shop. Go to the music section and hook up with the cute girl on the help desk. Begin by asking questions about non-existing bands.
Tips
Look in Time Out for free events.
Wander around a lot. Especially on the South Bank. You'll often see outdoor exhibitions, events and festivals, especially in the summer.
Eat at staff subsidized canteens (Selfridges, Harrods, many newspaper offices). I have not done this since 9/11 therefore security likely will be tougher now but there's nothing wrong in trying. Try to blend in with the surroundings, think of yourself as having a right to be there and don't blab too loudly (especially if you have an American accent). Play the dumb, glassy eyed tourist if caught "um, the guy at garden furniture told me to go here..." Chances are you get a decent meal at a cheap price.
Warnings- Buying food and drink in cafes around the tourist areas can be very pricey. Cheap eats are a real find and knowledge of good, cheep cafes and restaurants is often jealously guarded. Time Out do a cheap eats guide that can be of some assistance but if in doubt, and the weather permits, picnics are by far the cheapest option.
- You may just fall in love with that cute girl.
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