A Shrubbery, saith the knights who say nee! I guess that won't make much sense unless you have seen Monty Python's Holy Grail.....Seriously, though, I don't know that there is a specific term for it. In the South, it is called the yard.

Such gardens are usually referred to as peat beds. They're often constructed with low walls made from solid blocks of peat. The peat used to fill the beds is very coarse and solid - far different from the baled, dehydrated, and largely useless powder available in North America. The underlying rock in many parts of Britain is lime or as it is referred to there, chalk. Peat beds are necessary to grow acid soil demanding plants.

Ericacious garden since the ericaceae is the acid loving plant family.