Running cost is decided before the system is switched on. An inverter system draws hard while it pulls a warm room down and very little once it is holding temperature, so the number that matters is not the unit's rating but how long it spends at full output. That is a question about sizing, insulation and shading, and it is settled at survey rather than on the electricity tariff.
Cost of running air conditioner UK homes: rated power is not running power
A modern split system modulates. Its plate rating is the maximum the compressor can draw, and a correctly sized unit reaches that only while it is recovering a hot room. For most of a British summer day it is loafing at a fraction of that, which is why comparing plate ratings between units tells you very little about what either will cost over a season.
Is aircon expensive to run when oversized? Why a big system costs more
An oversized unit cools the air fast, satisfies the thermostat, and stops. Then it starts again. Each start is the expensive part of the cycle, and the short runs never last long enough to strip humidity out of the room, so the room feels cold and damp rather than comfortable. Oversizing costs more to buy, more to run and delivers a worse result.
How much does it cost to run an air conditioner? The building does most of the work
The load is solar gain through glass, heat through the roof, and the people and equipment in the room. Shading a south facing window, insulating a loft over a hot bedroom or closing internal doors changes how long the system runs far more than any setting on the remote. A system fitted into an unshaded glazed room will always run hard.
The winter half of the arithmetic: the cost to run air conditioner as a heater
A reverse cycle unit is a heat pump running the other way, and in a single room it can be a cheaper source of heat than an electric panel heater because it moves heat rather than making it. Whether that beats running the existing central heating for one room depends on the fuel and on how the rest of the house is heated, and it is worth asking an installer to explain their assumption rather than accepting a claim.
Other questions people ask
Is it cheaper to run one big unit or several small ones?
Several correctly sized units in the rooms you actually use will usually beat one large unit trying to serve a whole floor, because you are only conditioning occupied space. A multi split shares one outdoor unit between those heads, which keeps the installation cost closer to a single system.
Should I leave it running all day or switch it on when I get home?
For a well insulated room, holding a moderate temperature is often cheaper than a hard pull down every evening, because the compressor spends its time modulating instead of at full output. For a poorly insulated or heavily glazed room the balance shifts, which is why the honest answer is that it depends on the building.
Does the refrigerant need topping up?
A sealed system should not lose refrigerant. If it needs topping up it has a leak, and topping it up without finding the leak is both a waste of money and, for larger charges, a regulated failure. A drop in performance is the usual first symptom.
Does a service reduce running cost?
Yes, and mostly through airflow. Blocked filters and a dirty outdoor coil force the compressor to work longer for the same effect. A service that cleans both, checks the charge and clears the condensate is the cheapest performance improvement available to an existing system.