Being a college student, I'll be living on a strict budget during my time in London. That being said, I've researched some fun things to do in London that are also inexpensive.
1. Changing of the Guard
The Queen's Guard in London changes in the Forecourt inside the gates of Buckingham Palace at 11.30 AM every day in the summer and every other day in the winter. If you get there early enough, you can get a view of it from just outside the front gates.
2. Play in the rain or... not.
Contemporary Art Group Random International created a digital installation that gives visitors the chance to experience what it would be like if they could control the rain. In "Rain Room", the sound of water and moisture in the air gives visitors the impression of being in the middle of a lucid downpour - without getting wet.
3. Street Performers
In the West Piazza of the Covent Garden Market, street performers entertain visitors every afternoon. All of the performers are licensed, and they have to pass an audition to be able to perform there.
4. Take the Bus
£2 (With an Oyster Card)
There is no shortage of open-topped sightseeing buses in London, but why pay over £20 for a ticket when you can see the same sights for just £2? The route starts at the bus station of Liverpool Street station in the north eastern corner of the City of London and terminates at Fulham Broadway traveling via the West End and some of London's most famous landmarks including St. Paul's Cathedral, Fleet Street, the Strand, Trafalgar Square, Big Ben, Buckingham Palace, King's Road, and the Houses of Parliament.
5. Prince Charles Cinema
A tight budget doesn't mean that you can't enjoy a night out in London's famous West End. At the Prince Charles Cinema in Leicester Square you can see great films from just £6.50 on evenings and weekends.
6. Trafalgar Square
This iconic square has many sights to see including Nelson's Column and the National Gallery. It is both a tourist attraction and the main focus for political demonstrations. Every December, Norway donates a marvelous Christmas tree, to thank Britain for liberation from the Nazis.
7. Live Music
If live music’s your bag and you’ve got no money in your purse, don’t despair just yet, because London’s got more free gigs than you could ever expect to attend.
8. Indulge in a "Proper" Cup of Coffee
£1.89 (This varies from shop to shop.)
Amid the West End's sea of cappuccino merchants there are some very special coffee shop gems.
9. Find a Good Read
Explore one of the many book shops in London. The London Review Bookshop, The Big Green Bookshop, P&G Wells, Much Ado Books, and The Book Hive are just a few of them.
10. Museums & Galleries
London has over 300 museums and all of their major ones are free. The following is a list of free museums, but it's not complete. There are many other free museums in London.
Natural History Museum
National Portrait Gallery
The Tate Britain
Victoria and Albert Museum