Black cabs are a famous symbol of London (not all Black cabs are black - many of them are covered by colourful ads). Drivers are usually very reliable and are extremely knowledgeable about London’s streets (they have to pass an exam call The Knowledge - some spent 2-3 years to know every street in London and how to get A to B). By law black cabs must be licensed and carry a meter. Fares are higher after midnigh and weekends. Add 10% for tips.
Minicabs are usually cheaper than black cabs. especially in the night or over weekends. But minicabs are unlicensed and are not allowed pick up customers in the street. Check Yellow Pages or ask hotel front desk for local minicab firms. If you going to train station or airport in odd hours (midnigh or early morning), you should book a minicab in advance. Minicabs usually charge a fixed price for most destination so ask the price when you book them.