iPhone 3G delayed SMS and voicemail delivery

I live in London, and have already disabled 3G on my iPhone 3G as a result of reports of network capacity issues for data.

Today, I turned the phone on, and at 1400 I received a phone call. During the call, the phone received two SMS, one from 0630 that morning, and one from 1130. It seemed like receiving the call had "woken up" the phone and the messages would have been delayed somewhat indefinitely had this call not come in.

At 1430, I received notification of a new voicemail. The phone had never rung (I had the phone sitting on my desk right in front of me all day), the voicemail had been sent at 1330, and was from my son's school notifying me that he'd been sick and needed to be collected ASAP.

Needless to say, these delays are simply unacceptable, and I'd like to find out if this is a network or a handset issue. I'm running OS 3.1.2, and have 3G disabled.