I was in a similar situation a couple of years ago - I had my line rental with BT and my broadband with Orange. Started getting hassle off BT over something and nothing and did not like their attitude so I phoned Orange and switched my line rental to them. Have had the total package with Orange since and never had any trouble whatsoever, in fact I recently advised my parents to switch to them as well as they were very unhappy with BT (they had taken some money from their account when they should not have and were generally mucking them around), the switch over went very smoothly and they are very happy with the service.
I was told that it did not count that I had a PAYG mobile with them, it had to be one on a contract to apply for the discount.
I would definitely get in touch with them to switch (rather than them phoning you).