Elizabethan London used both coal and wood for it's fuel needs. There was a strong preference for wood instead of coal, but early modern London often substitued coal for wood, where possible. The main problem at the time with the use of coal is that it was generally burned in a open fireplace, rather than in an enclosed stove, which led to much worse indoor air quality.

I don't have any reliable numbers for fuel consumption in the Elizabethan period, but I know that by 1650, London was already importing over 325,000 tons of coal a year, and had a population of over 300,000 persons. So we can say that by the middle of the 17th century, London as a whole was already consuming about a ton of coal per capita per annum. This fits in with our understanding pre-modern economics, where most households consumed between one and three tons of fuel-wood per person per year. As early as the mid-1300s, London had already largely exhausted it's local forests, and increasingly had to wood from farther than farther away. It was in this context that coal began to be shipped in from Newcastle, and also from Wales and the Bristol watershed.

Most urban households did not have the storage capacity to store more than a few days worth of wood or coal, and probably took delivery via wagon or barge of fuelwood or coal once or twice a week. This refers only to households, of course. Some commercial enterprises, especially bakers, brewers, and pottery, consumed enormous quantities of fuel, and needed more fuel delivered at least daily. We know that by the mid-1500s, London's brewers presented a petition to the authorities that they be allowed to import more coal; they were already conuming over 20,000 wagon loads (about a ton?) of wood a year, and were going broke with rising wood prices.