I had the same problem with the MINI insurance.
I was under 21 (due to be 21 in a few days) - When I asked if I could wait and then get it, I was still denied because I needed 2 years no-claims.
The person on the phone was very nice though, wished me happy birthday and apologized for not being able to help. They use the same underwriters as Egg insurance I believe, who have the same rules.
I'm now over 21, have the no-claims AND my insurance is up for review so I may look into them.
MCS's like to cost young drivers a lot of money (understandably so though).