Rose Standish Nichols writes in her 1902 book English Pleasure Gardens, just reissued: “Grottoes or artificial caves [in the gardens of early Rome] cooled by streams of fresh water served as musea, or thinking-places for philosophers, where they could meditate in solitude, hidden from observation, protected from interruption, and sheltered from the heat of the midday sun in summer.”
Stourhead has its own grotto as well, built in the eighteenth century. The English of that period showed their affection for Italian garden design, even in the rocks of a grotto.
Italian garden design was important to the English, just as the English design became important to American gardeners in the nineteenth century with the help of the seed and nursery industries. It still is today.