I had connections within 45 mins of arrival at CPH, usually they are OK (so long as there is no passport control). Also, 45 minutes connections are not that uncommon if you transit through VIE. Usually they have 30 minutes or so buffer time since they anticipate problems at LHR.
That said, if there are problems in inbound, there is a very good chance of you missing the flight, especially if it comes from LHR. However, there have been a couple of instances where they delayed the flight until my flight landed.