It will cost you about £10 per year if you leave it on 24/7.
In order to get the best connection you are best to leave it on 24/7 however if you really want to you could power it down over night but as you can see, the cost of leaving it on spread over the year would be negligible.
This might also be of use.
http://bt.custhelp.com/app/answers/detail/a_id/11353/~/what-is-bt-power-save%3F