From my brief searching through the Apple discussion sites, it looks as though you can't actually delete an iCloud account!
Here are some links to some posts I've read regarding this:
According to the answers from people with fairly high credentials for the above questions, it isn't possible. The only option you have is to disconnect your device(s) from iCloud and just stop using it unfortunately.
The reason you provide for not using the iCloud account though is because of bombardment of emails from services you have subscribed to. I suggest a 'block sender' use on your email client whatever that may be, or alternatively the option suggested by @patrix. Also, most of these types of emails I have found have an 'unsubscribe' link at the bottom of their emails, so you should also probably look for that on some of these emails.
Hope this is of some help!