Net-zero policy targets will require a transition from conventional vehicles (CVs) to greener alternative fuel vehicles (AFVs). This paper examines what influences the demand for AFVs and CVs in the UK's large automobile market, looking at vehicle attributes, prices, and other factors, such as brands, country of origin, car segments, and vehicle equipment. Using an extensive, unique dataset covering the period 2008-2019, we compute own-price, cross-price, and demand elasticities for CVs and AFVs. Applying a random-coefficient discrete-choice model of demand, and controlling for consumer heterogeneity, unobserved product characteristics, and price endogeneity, we find that the key drivers of demand are prices, fuel consumption, and vehicle size, with similar demand sensitivity between CVs and AFVs. Demand falls by 3%-5% for a (sic)1,000 increase in price for both CVs and AFVs, conditional on the quality and availability of substitutes. This indicates that UK consumers are not willing to pay a price premium for AFVs, suggesting little value placed on the "greenness" of AFVs. We estimate that a (sic)1,000 subsidy to AFV purchases would lead to 4% of consumers switching to the greener vehicles. While CVs and AFVs exhibit similar price elasticities, vehicle size affects AFV demand by about 40% more, as their purchasers value smaller sized vehicles. Our results indicate that without financial incentives, the uptake of AFVs may remain low, as the higher cost and lower convenience the environmental considerations for the of consumers.