EH chief executive Dr Simon Thurley said: "It's the most ambitious fundraising project of its type taking place in this country. It's the first time anyone has ever tried, on a scholarly basis, to recreate an Elizabethan garden."
The £2.1m project is funded by the Wolfson Foundation, a grant-making charity. The garden is being reconstructed to represent how it was in 1575, when Robert Dudley, earl of Leicester, entertained the Queen on her "summer progress".
Thurley said: "Because of the ludicrous extravagance of the visit, which incorporated mock battles, bear baiting and masques, information about the garden was recorded and that is why we can recreate it."
EH is using a letter from merchant Robert Langham, which describes the garden in great detail. Features mentioned that are currently being constructed include an 5.5m-high marble fountain and a bejewelled aviary.
Exeter-based contractor Rok is overseeing the build, with timber work sub-contracted to McCurdy & Co of Reading, groundworks to MTB Groundworks and fountain construction and carving to Fairhaven of Anglesey Abbey.
Newly appointed head gardener Fiona Sanders began planting the knot garden last month to a design based on a 16th-century engraving by Dutch architect Hans Vredeman de Vries. Yews, juniper and bay have been used and will form topiary.
Heritage varieties of strawberries, thrift, Dianthus and Calendula have been brought in from nurseries including Allwoods and Coolings. Sanders said the charity is trying to use primarily UK nurseries.
EH head of gardens and landscapes John Watkins said they are still searching for a clove-scented carnation available during the 16th century and that anyone with any leads should contact the conservation charity.