London can be expensive with entrance to most places (even a visit to St. Paul's Cathedral) is $20+ dollars so I decided to mostly walk and enjoy the architecture and buildings rather than enter costly tourist traps.
You'll need a good pair of walking shoes and before you leave home, order an Oyster card which you can use on both buses, mainline trains and underground in and around London. You can add funds to the card at most stations. Take a water bottle with you. You can also purchase an inexpensive pocket map at most souvenir shops.
Tour of East Central London
Begin at London Bridge Railway Station (Both underground and mainline trains arrive and depart from here)
Note: If you prefer to go directly to sites rather than walking, there are plenty of underground stations and bus stops along the way.
Cross the River Thames via London Bridge (there are good views of Tower Bridge and the HMS Belfast from here). Keep walking along King William Street and you will come across The Monument on your right (Monument Street/Fish Street Hill). The Monument commemorates The Great Fire of London in 1666. If you feel energetic you can walk up the 311 steps to the top which affords great views of London. The cost is around $6 for adults (cash only).
Turn left on to Cannon Street which will become St. Paul's churchyard. To the right of the church take New Change Street which becomes St. Martin's Le Grand and leads to The Museum of London (free entrance).
Take note as you are walking that there is a Tesco mini market which is a great place to buy lunch (three pounds for a sandwich, chips/crisps and a drink). Across the street is St. Paul's churchyard - a great place for a picnic.Note: many of the supermarket chains have mini markets so look out for those but they can be very crowded at lunch time.
After viewing the museum return to St. Paul's Cathedral and directly opposite is Peter's Hill which leads to the Millennium Bridge (pedestrian bridge). Cross the River Thames to the Tate Modern Museum (there are free displays if you don't want to pay for any of the exhibitions). Be sure to look for the toilet constructed of mirrors in which occupants can see out but others can't see in!
Continue along the river, returning to London Bridge Railway Station, where you will pass a replica of Shakespeare's Globe Theatre, a replica of the Golden Hind - Sir Francis Drake's ship and Southwark Cathedral. Southwark Cathedral is worth stopping and viewing and if you haven't yet eaten, is a great place to sit in the gardens after purchasing food at a nearby eclectic selection of stalls. A little farther on is the Borough Market where you can buy fresh produce.
Note: The Shard is a good place of reference when trying to find your way to London Bridge. It's quite expensive to go to the top but affords spectacular views.
