There are ways to travel, and then there are ways to travel. England has them all.
Wherever I go, I like to use public transportation. You may see places that you have not noticed before, you might strike up a conversation with a local with broad knowledge of the area, and you will probably pay less to get from one place to another. However, make the effort to take at least one big, beautiful taxi ride while in London. They have some of the best drivers in the world! May you have safe travels, always.