When I first got an iPhone 4s on BT I used this this link to change the settings for MMS / internet. It was all fine for a while but for some reason now I can still access the web but MMS messages fail. I suspect it stopped working around the time I upgraded to IOS6 but I can't be sure. I've tried the settings a load of times and also restored the phone to factory and entered the settings without restoring from backup but no with luck.
Take the SIM card out of the phone for at least an hour as the SIM can accumulate some cache from previous useage which might promote a conflict, in your case between two handsets. Before you take the SIM out, wipe all the settings in question from the device. Once re-installed into the device, input the settings again.
If you're sure your settings are correct, contact BT mobile and ask them if your account is [still] provisioned for MMS.
While you are onto BT mobile, ask them to confirm the [current] MMS settings for your SIM card and any extra's for the i phone you might need to know about.
Last stop then IMHO is to ask for a replacement SIM card because you think on the basis of the tried and failed above, that the SIM has become faulty.
AQ. "Welcome to Royston Vasey - You'll never leave."