Is any body know about London cab services, I want to book cab from Gatwick to Liverpool St (EC2)
In London there basically are two types of 'cab' services: black cabs and mini cabs. The former ones are the official taxis, which you can flag in the street and then pay for them by the meter. The latter ones you need to book in advance and you agree the price up front at the time of booking. They are not allowed to pick you up without booking. Mini cabs are usually cheaper, especially for longer distances.
In your case, you most likely want to book a minicab. There are hundreds of different companies offering this kind of service. One of the bigger ones is Addison Lee. You can find a lot of others in Google, or probably there are some advertisements on Gatwick Airport. The prices may vary substantially between different companies, so it is worth doing a quick search before you leave. Some companies now offer quotes online, which makes it easier.