Reddit mentions of Listed Buildings, Conservation Areas and Monuments

Put simply if you're working in the operational area the work you are doing is more about managing people and projects rather than the heritage itself. Heritage legislation is fairly easy to learn, all you need is a copy of Charles Mynors, and to understand how to deal with conservators and the like. In terms of site management of a historic house, you're going to be involved in organising projects in order to bring visitors and money onto the site.

I would recommend the heritage management courses - for instance the one at York - if you're looking to do interpretation and so on, but even then it's better to specialise in a particular area, so that you can better research sites in order to produce material on them. In that the building history one I linked at Cambridge below has some good career potential - for instance in Historic England's listing department.

If you haven't done so already, I strongly recommend having a look at the National Trust careers site to give yourself an indication of what kinds of qualifications they are looking for and factor that into your thinking. EH one here too.