The whole point of a router is to share a bb connection between several computers. So put away your old router and use the new wireless one to provide the connection for both your computers (I'm guessing it's a desktop and a laptop?)
As said by others, you cannot connect two modems to a phone line at the same time. BT don't need to know what you have, nor do you need permission to change your equipment, so long as it has the the relevant green circle to say it's certfied for use in the UK.
If you don't want to dump your old router, then the best way to add wireless capability is to use a wireless access point. But given that you're asking this question, I'd suggest that an all-in-one wireless router will be less problematic to set up. And furthermore, if your present router has only one ethernet socket, then you'd have nowhere to plug in your desktop machine.
______________________________________________________________________
http://www.vfast.co.uk/ - 2 Mbps symmetrical via fixed-link wireless