how does the cost of taxi's tend to run in London, compared to NYC? also is public transportation safe at night?

New York taxi fares are cheaper than almost any other major city. Have not been to London in three years but at that time London fares seemed about 1/4 to 1/3 higher than New York.

I'm sure if you go to the BTA web site they will have exact info.

The tube and buses will be perfectly safe anytime/place a tourist is likely to be. You can safely ride the tube or buses after the theatre or late night meals. Taxis are fairly expensive - but since the tube is so convenient, if you are on a limited budget you can save a taxi ride just for a "splurge" experience. Every visitor should take a London Black Cab at least once. London cabbies - and the cabs - are terrific. Nothing like the nasty Yellow Cab sedans in most N Amer cities. (BTW - London "black" cabs are not all black - every color under the rainbow)

More detail than you may wish to know from the horse's mouth at
www.tfl.gov.uk/pco/

Taxi's in London are very expensive
as with most costs expect to pay
50% more then in the US

And expect 100% more courtesy and friendliness.

The buses and Tube are so convenient, we've never had occasion to take a taxi, even though we intended to "just for the experience".

I agree. Other than arriving back at the train station at 1 or 2 in the morning from Stratford -- too late for the tube, we took a taxi. We went a long way round to get to our place in Covent Garden and the driver, when I questioned him, said it was due to the traffic. What traffic?? It was dead as could be everywhere.

Taxis are rather expensive in London.

The tube is safe especially if you're staying in the Central London area.

London taxis are great, if not cheap, and the drivers are exctremely knowledgeable. They have to be in order to get a license, as they need to pass an exam that requires detailed knowledge of the London streets gained only by experience and long, hard study.

As for the underground, there are one or two stations that I wouldn't want to find myself in late at night--but in general there's no need to worry.