It's quite possible for broadband to still work even if a line or exchange fault is causing the telephone service to fail.
Before calling BT, you need to establish that the problem is not on your premises. Hopefully you have a modern master socket (NTE5A), like this:
http://www.austin-taylor.co.uk/images/nte5ext. jpg
Undo the two screws and withdraw the lower part - you'll see a socket inside - plug a phone in and see what happens. If it works, you've something wrong in the house. If it doesn't, you can report it to BT safe in the knowledge that you won't be charged.