Did the modem problem coincide with the "outage" in your area or did it start after that.
Have you checked to see if your neighbours are having and "outage" and also checked on the status page.
I would contact BT now and report the modem as a faulty. This is over and above any "outage" that they claim. The reason I asked you to check the status page and neighbours is that it has been known for Call Centre staff to blame an network problem when in fact there isn't one.
Another option could be to get a replacement one ? (Loads on that well know auction site).
Which would be quicker than waiting for Openreach to turn up or its not worth the time/stress of waiting around , time of work ect
'Another option could be to get a replacement one ? (Loads on that well know auction site).'
Why should he have too, the DSL Modem, like the NTE is the responsibility of Openreach. If it breaks they need to come and replace it.