There were trees, and flower-beds, and evergreens clipped into strange shapes, and a large pool with an old gray fountain in its midst.

But the flower-beds were bare and wintry and the fountain was not playing.
This was not the garden which was shut up.

How could a garden be shut up?
You could always walk into a garden.
She was just thinking this when she saw that, at the end of the path she was following, there seemed to be a long wall, with ivy growing over it.

She was not familiar enough with England to know that she was coming upon the kitchen-gardens where the vegetables and fruit were growing.

She went toward the wall and found that there was a green door in the ivy, and that it stood open.