Some ISPs won't allow emails to be sent with anything other than their own domain name, others have no restriction providing you are logged on from their connection and the rest will allow you to use other domain names if you request it. The server you send your mail to is a relay and it needs to know that the relay facility is not being abused, hence the restriction. Those nasty spammers spend much time trying to find unrestricted relays so the spam cannot be traced back to them!
Ask BTInternet if you can use another domain name. If not use one of the hosting companies to host you domain and then send your mail through them. I have used 34SP for some time now for various domains and have no complaints.