RedCare is BT's alarm line service. It's monitored in such a way that if it were to fail/be cut BT immediately inform the keyholders.
I've not done anything with redcare myself, but I would think that having one line might be a case of all your eggs in one basket. If that redcare line goes down or is put in use by one alarm then I imagine the other systems wouldn't be able to call out.
I'd have a word with your alarm installers and see what they think.
