sam007 is not reporting a problem with email delivery, but rather with Barclays atypical practice of not automatically generating an email notification when an e-statement is generated. Enrolling in automated payments for every account provides free insurance.
Sadly automatically paying a bill that could have fraudulent charges without looking at it never seemed to be a very good option for me!
It is entirely reasonable to assume that if you ask for paperless statements you WILL get a statement (or notification of same) WITHOUT having to say you want one.