I suppose it depends on the extent of your dependence on it? For example, I am a graphic & web designer so broadband connection is vital to my business as I'm based at home. If I am working at home I am generally using it all day. If I'm out of the 'office' at a client's premises all day it is not being used for personal use either so I can safely claim the majority if not all of the costs of the service.
As you say, you work away from home, so you could perhaps purchase mobile broadband from one of phone providers and claim the full amount as an expense. However, as you don't work from home, then justifying the full costs to have the service at home might be difficult.