London is well known for its black cabs. In every movie that plays in London you will see them. When you visit London, you should at least travel in them once.
With regards to taxi's in London you have to be very careful. When you arrive at airports and international train stations, you may be approached by someone offering you their services. If someone walks up to you this way, it is not advisable to use him or her. Most of the time they will be illegal. First of all they might rip you off, but also, most of them are not insured. If for instance an accident happens during the trip, you could not claim for any personal injuries, damage or any other costs.
If you travel by taxi, first of all check if the taxi you are going to use has a license. On the back of the cab there should be a plate with the text 'Taxi license' and a number on it. If not, it is either a minicab or an illegal taxi. With regards to minicabs, British Government apparently has decided that minicab companies that comply to certain regulations (insurance is one of them), can get a license too.
A while ago, a woman used what she thought was a black cab. However, the driver was not a real taxi driver, but had bought the taxi second hand. These taxi's do not have a license plate anymore, but the woman did not know this. She got sexually assaulted and was left behind for dead. As far as I know she survived and was able to describe the man, who got arrested. I do not want to scare you off with this last bit of information, just warn you to really careful look for the driver's taxi license. It is better to be safe then sorry.
Also, I advise you to ask for a quote (or estimation) first. Tell the taxi driver where you want to go and he or she should be able to give you a rough idea of the costs.
Please do not let my comments above completely put you off from travelling by taxi. Most of London's taxi drivers are quite reliable. As always, it is a small group of people that give the rest a bad name. With regards to the licensed taxi's, if you are not pleased with the way they treated you or the amount they charged you, you can always note their license number and file a complaint. However, keep in mind that travelling by taxi will costs you approximately a pound per mile on top of a basic fee.