"he meets her in Groppi Park - beside the heavily watered plum gardens"

Groppi Park may either refer to the Groppi tea gardens, or the 'french pleasure gardens' of Cairo, like Ezbekiya Garden, which you can read more about here.

“During WWII, Groppi’s on Adly Pasha Street (a second branch of Groppi’s) was frequented by members of Britain’s Eighth Army and was a favourite of General Montgomery, who came to enjoy jazz evenings in the garden,” says Adel Toppozada, former Deputy Minister of Information and grandson of former Egyptian Prime Minister Hussein Pasha Rushdy. (Source).

Images of Old Cairo