Will I be able to keep and use bt router?
Depending on how long you've been with BT, you may get an email or letter asking you to return your old router. Even if you are able to keep it won't work with your new broadband service. It is however possible to hack a BT router to make it work with other providers but it's pretty advanced stuff and probably not something you'd be able to manage.
Are there any issues re installing Utility Warehouse router?
No, simply plug the Utility Warehouse router in and it should work. The wireless name and password are printed on a label on the back of the router and you'll need to enter those details in your phone and tablet.