There are two very different pricing models on London’s roads, and knowing which one you are paying is the single most useful thing when it comes to cost. A black cab (a Hackney carriage, the type you can hail on the street) runs on a taximeter set by Transport for London. The meter starts at a minimum fare and then climbs based on distance and time, using one of three tariffs — Tariff 1 for weekday daytimes, Tariff 2 for evenings and weekends, and Tariff 3 for late nights and public holidays. Because part of the fare is charged on time, heavy traffic directly increases what you pay.
A minicab or private hire vehicle (PHV) works differently. It cannot be hailed on the street and must always be booked in advance, but in return the operator can give you a fixed fare for the whole journey before you travel. That is how Airport Move prices work: you enter your pickup and destination, receive a set price, and that price does not move — regardless of traffic, the time of day, or how many flights land at once.