It is widely accepted that young drivers will have to pay higher premiums on their car insurance. Insurance providers consider 17-25 year olds to be the highest risk group of drivers on the road. Because of your lack of driving experience you are more likely to be involved in road accidents which mean you are more likely to make a claim.
Many companies will not offer temporary car insurance to anyone under 25, let alone 21 and most will not offer to 18 year old drivers at all. However, there are a growing number of companies that have considered lowering the age limit on temporary car insurance.
It may take a bit longer, but you are still likely to be offered a car insurance quote by a number of companies if you are sure in your mind what you need from your policy.