The story of King James I importing mulberry trees to start a silk industry is often told, but London's mulberry heritage goes much further back in history.
Londinium
Mulberry trees are not native to England, so mulberry seeds found in excavations of Roman settlements near the Thames suggest that the Romans planted black mulberries for their fruit. The berries perish soon after being picked, so could not be imported. In this case, mulberries would have been growing in London before the 5th century CE.
Medieval plantings
Black mulberry trees were planted in medieval monasteries and abbeys, probably for their shade and fruit, often in the infirmary garden.
Henry VIII
When Henry VIII cut off links with the Catholic Church in order to divorce Catherine of Aragon, he closed and ransacked the (Catholic) monasteries. Their mulberry heritage was often lost at the same time.
Elizabeth I
The nobility prized the shade and fruit of the black mulberry, often as one-upmanship. If you wanted to impress your peers with exotic mulberries on the table, you had to grow them yourself. Some Elizabethan black mulberries are thought to survive today in stately homes like Syon House and Hatfield House.
King James I of England
Italy had a thriving silk industry from the 13th century and France from the 15th century, using both black and (predominantly) white mulberry leaves to feed their silkworms. In letters of 1607 and 1608 King James I of England asked the nobility to plant 10 000 mulberry trees to support an English silk industry to rival that of the continent.
Silk production didn't take off in England, though, perhaps because black mulberries were planted and not white, which produces finer silk. Perhaps the cool, damp climate wasn't right. James did plant thousands of white mulberries in Virginia, though, where the tree thrives, but this colonial silk production still didn't take off.
Huguenots
The revocation of the Edict of Nantes in 1685 brought many Huguenot (Protestant) silk weavers to England fleeing religious persecution. Many settled around Spitalfields in East London, bringing their skills with them. By the early 18th century England had a thriving silk industry, using imported raw silk - so no need for mulberry trees to feed silkworms.
Today
In the 1930s Lady Zoe Hart Dyke started a Silk Farm in Lullingstone Castle, Kent, later moving it to Ayot St Lawrence in Hertfordshire. At its height the farm had a 20-acre plantation of white mulberries to feed thousands of silkworms, breeding in 30 rooms of the house. Silk from Lullingstone was used to make the late Queen Mother's coronation robes in 1937, Queen's Elizabeth II's wedding dress in 1947 and her coronation robes in 1953. The Lullingstone mulberries seem to have been grubbed out.
Wilkin & Sons have a large black mulberry orchard at their Tiptree Farm in Essex, producing mulberries that are hand-picked to make jam today.