Given the option of having costs automatically taken from a credit card (as opposed to like with BT where when your bill arrives you call them to make payments) or paying by Direct Debit, which is better? I'm with a new company that takes payments straight away on a regular basis, you register your card with them, and it's all done automatically. Bit new to this way of paying and wonder if there are any better safeguards changing to the Direct Debit option? Any help would be appreciated.

I never use continuous credit card authority now - I read THIS and MSE and changed to Direct Debit immediately.

If I changed to Direct Debit with them then decided I was going to run away (a logical enough step when you've just registered with a certain telecommunications provider ) then stopped the Direct Debit payments, would they be able to then steal money from the credit card registered with them earlier?

You are covered by the Direct Debit Guarantee with direct debits. Not with CCCA. Direct debit is a much more safer way to pay.