there is a round london sightseeing bus,which stops at all the main attractions,you just hop on and off,petticoat lane is near liverpool st station and aldgate station.
Get a travelcard and use all the buses and tubes you want. There's also a very fast boat called the Clipper which zaps along the river between the Canary Wharf area and Charing Cross, stopping at lots of places in between. You can get a travelcard for this, or pay per single journey.
A zone 1-2 travelcard costs about �4.80 a day (starting after 9.30am) and covers most of the sights. It's good for tubes and buses, but I don't think for the sightseeing buses. Buses can be quite slow (though the views are good, especially from upstairs), so if you've got a lot of ground to cover, use the tube.
I would give Petticoat Lane market a miss - just full of tat. Suggest you go to Camden market for a true variety. Agree with NORMANTHEDOG, use the bus. I used the tube on Friday and got stuck on northern line for 20 mins, nearly got cooked.
Suggest getting the #11 bus - goes from Fulham to Liverpool Street and past the main sights of London. Best cheapest way to see the city http://en.wikipedia.org/wiki/No._11_bus
If you are in London more than a day get an Oyster card - available from all underground stations - you can put �20 on it and it should last around 3- 4 days depending on usage - unlimited travel on all LRT buses and underground