The Tourist Information UK website tells us, briefly, about the maze:
The maze at Hampton Court was designed and planted in around 1700 by George London and Henry Wise for William III. It is possible the current maze replaces an earlier one on the site.
It was originally planted using hornbeam and latterly replanted and repaired using yew. The maze covers a third of an acre and has half a mile of paths. It is the UK's oldest surviving hedge maze.
The Atlas Obscura website tells us about the maze at Hampton Court:
The Hampton Court hedge maze is the oldest surviving hedge maze in the United Kingdom, a multicursal (unlike a labyrinth which is single path or 'unicursal' in a maze which is 'multicursal' a visitor must make decisions) puzzle maze baffling and delighting visitors since the 17th century.
While it isn't nearly as large as modern day mazes, it still provides a challenge and remains an important historical structure. The original design has since been modified due to gaps in the hedge, offering more ways to the center and more wrong turns, some of them ending in loops. It is constructed on a third of an acre, with half a mile of paths, within 60 acres of riverside gardens.
Planted by George London and Henry Wise for William III of Orange in 1690, evidence points towards the current maze having replaced an even older one, possibly devised for Henry VIII or Thomas Cardinal Wolsey. The maze is now the remnants of what was once the many winding paths of William III's 'Wilderness Garden'. Initially comprised of hornbeams, the maze has since been repaired over the years and was completely replaced with yew in the 1960s.
A project to restore hornbeam to the maze has been introduced, with hornbeam recently planted in the center to ascertain its viability in modern day wear-and-tear conditions. Unique at its time of development, the Hampton Court Maze provides multiple path choices and dead ends, whereas research shows that previous hedge mazes were unicursal, with only one path leading to the center.
There are several accounts of people losing themselves in the maze, both in literature and reality. One of the most popular, if exaggerated, accounts of navigating the labyrinth is given by 19th century British humorist Jerome K. Jerome in his 1889 novel "Three Men in a Boat." He describes one character studying a map of the Hampton Maze, announcing it should hardly be called a maze, as it is so simple. The three men proceed to haughtily navigate the puzzle, only to become lost and circle around the center repeatedly until they had to call for the groundkeeper's help.
The Hampton Court Maze takes an average of 30-45 minutes to complete, and though it is an 'island maze' which contains separate sections causing this technique to not normally work, the hedges are grown in a fashion where placing and keeping one's right hand along a wall will lead them to the center.
A recent addition to the maze is the audio exhibit entitled Trace. Spread across the hedges is a gentle 'soundwork' composed of music fragments, snippets of conversation, the rustle of fine silks, and tantalizing laughter that disappears upon turning corners; aimed at luring visitor's down certain paths, Trace is a permanent art installation that will eventually incorporate one thousand generated sounds.
Wikipedia has an article about Hampton Court Maze with most of it taken up by the reference to it in Jerome K Jerome's book "Three Men in a Boat":
Hampton Court Maze is a hedge maze planted some time between 1689 and 1695 by George London and Henry Wise for William III of Orange at Hampton Court Palace. The maze covers a third of an acre and contains half a mile of paths. It is possible that the current design replaced an earlier maze planted for Cardinal Thomas Wolsey. It was originally planted with hornbeam, although it has been repaired using many different types of hedge.
The maze is in 60 acres (0.2 km2) of riverside gardens. It has been described by many authors, including Defoe, and the humorist Jerome K. Jerome, who wrote in Three Men in a Boat:
"We'll just go in here, so that you can say you've been, but it's very simple. It's absurd to call it a maze. You keep on taking the first turning to the right. We'll just walk round for ten minutes, and then go and get some lunch."
...Harris kept on turning to the right, but it seemed a long way, and his cousin said he supposed it was a very big maze.
"Oh, one of the largest in Europe", said Harris.
"Yes, it must be", replied the cousin, "because we've walked a good two miles already!"
Harris began to think it rather strange himself, but he held on until, at last, they passed the half of a penny bun on the ground that Harris's cousin swore he had noticed there seven minutes ago.
Jerome exaggerates the hazards of the maze. The maze has relatively few places at which the path forks and at all but one fork (in Jerome's time) the wrong choice led to a dead end at the end of a short corridor. There are many larger and more elaborate mazes nowadays. Recently, three new forking places (not shown on the plan displayed just outside the entrance) have introduced more possibilities of walking closed loops within the maze. The maze can still, as Harris stated, be threaded from entrance to centre and back by the method of always remaining in contact with the wall on one's right. This method guides the traveller into (and then out of) some dead ends and is thus not the shortest path. Topologically, this is a depth first search algorithm.
In 2006, arts group Greyworld were commissioned to create a permanent artwork for the maze. Their installation, a sound work triggered by hidden sensors embedded in the maze walls, is titled Trace. The maze has also been mentioned in Carol Shields' 'Larry's Party'.
A Bing bird's eye view of the maze can be seen here.