My brother lives in London right now. He's been for about a year so far. I visited him last Spring for a week.
To get around, you don't need a rental car. The Tube (subway) is really good over there. It's not quite NY, but there are enough stations that getting where you need to go is never more than a 30 minute walk.
As for price...most everything over thing is about the same price in pounds as it is in dollars. But, you have to remember that the pound is about 1.4 dollars, so everything is roughly 40% higher. You'll see value meals at McD's (I use McD's value meals as a good measure of how expensive somewhere is) at 2.99 or 3.99 #s, but that means $4.50 - $6.00 in dollars. I remember seeing those scooters that were popular here while I was over there. I remembered Walgreens had them on sale before I left the states for $39.99. I saw the same scooter in a shop for 39.99 #s, so there again, you're looking at about $55.00-$60.00 in dollars. So, it can be expensive. If you are buying anything big, though, you can get the VAT (sales tax) back when you leave. So, that knocks off 17% any big purchases you might make.
I would suggest not getting a car. Also, most of the museums over there are free for the last hour or hour and a half, so I generally tried to save a few dollars and hit those late in the day.
If you go, make sure you go to the Tower of London (great!), Westminster Abby, St. Paul's Cathedral, Tate's Modern Art Museum (next to Shakespear's Globe), British Museum (free; resetta stone and lots of stolen Roman and Greek items), Trafalga Square (sort of like Times Square) and as many pubs as you can during the evening.
Cool thing about London-ers...unlike here in America, people over there hit the pubs right after work. In the states, people don't normally go out till 8, 9 or 10. Over there, people start hitting the pubs on their way home around 5:00 or 5:30. Last call in pubs is 10:30 (they close at 11:00), but you can find clubs and jazz joints that are open later. I really liked this aspect. We'd hit a pub at 5:30, drink for a few hours at a few different places, and then head home around 11:00 or so. Makes getting up the next morning alot easier for the normal person over there.