I presume you want the address of your router while you are away from home rather than your computers IP address because that will be switched off. As far as I am aware this is not shown on MyBt or if it is I can't find it, nor is it when you login to BTYahoo. It only shows the IP address you are presently at. No doubt if I am wrong somebody else will correct this.
I found this on the Microsoft site which may point you in the right direction:
While you're still at home and connected to your home network, open a web browser and search for "find IP address" to find a service that will report your router's public IP address. Unfortunately, some computers are given a different IP address each time they connect to the Internet. An Internet service provider (ISP) can use a few IP addresses to serve many customers that way, but it means that your computer's address on the Internet is always changing.
To get around the problem of a frequently changing IP address, try a DNS dynamic update service, which allows you to assign a URL to your router that you can use instead of an IP address. The URL stays the same no matter how often the IP address changes. To find a service, search for "DNS dynamic update" on the Internet.
