From my experience with changing Android phones, the BT account updated itself once the original SIM card was working in the new phone. I can't remember how long it took for the information to actually update though - maybe overnight?
Thanks, good to know. I’ll report back, but there isn’t much content or many apps for me to restore from backup, so it shouldn’t take long.
Yes, I needn't have worried. Bought the new iPhone yesterday and restored from iCloud backup. My BT account shows the new phone and new IMEI this morning. Result!