Getting anonymous SIMs is trivial, 50p cash at Asda gets you a SIM with 10 minutes, 9 texts, and some data, included. It's like you just use one, burn it, and switch, without topping up.
But it needs to be in an anonymous phone. Where can you get a cheap phone for cash with no details given? I don't care about features, my current punting phone is an iPhone 3G which is so slow now it's crazy compared to current iPhones, but it doesn't matter as I use it for nothing other than text/call. But it's known to be my phone, so it's not anon.