I thought that but the guys on the phone (three separate calls, I might add...) insisted there were no network faults in our area. Plus my phone had been working fine until we were told to turn it off and switch sims.
But I still wondered if that might be the case and, lo and behold, we drove a mile down the road and both phones work fine. Glad there's no problem with the phone, but annoyed it took 45 mins on their 5p a minute line to confirm our original suspicion (and the problem only happened on my phone AFTER we changed sims).
Still, case closed!