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.

This was not the closed garden, evidently, and she could go into it.
She went through the door and found that it was a garden with walls all round it and that it was only one of several walled gardens which seemed to open into one another.