Question: Lady Margarita Elizabeth Rose Alleyne Armstrong-Jones is the only daughter of an English furniture maker who is 18th in line of succession to what?  

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Jacob Cress: Jacob Cress (born 1944, Norton, Virginia, United States), better known as Jake Cress, is a furniture maker in Fincastle, Virginia who is known for his interpretations of classical 18th century furniture.  He considers himself to be a cabinet maker and not an artist.  He also builds normal classical furniture, miniature furniture, and carves boxes, as well as decorative pieces.  He also restores furniture.  Additionally, he builds more modern pieces like country tables and desks.  Cress works with mahogany, walnut, and cherry woods.  His animated works include "The Decorator," "Alladin's Lamp," "Hickory Dickory Dock Clock," "Self-Portrait," and "Clock Face."  Cress crafts each piece of furniture by hand in his shop without sketching the furniture before he begins working on it.

Sheraton style: Sheraton is a late 18th-century neoclassical English furniture style, in vogue "ca" 1785 - 1820, that was coined by 19th century collectors and dealers to credit furniture designer Thomas Sheraton, born in Stockton-on-Tees, England in 1751 and whose books, "The Cabinet Dictionary" (1803) of engraved designs and the "Cabinet Maker's & Upholsterer's Drawing Book" (1791) of furniture patterns exemplify this style.

Arthur Brett and Sons: Arthur Brett and Sons is an English furniture maker.  The company was founded in Norwich, Norfolk in 1870.  The company creates bespoke furniture and architectural interiors such as paneled rooms and libraries.  The antiques arm of the business became a separate business and closed in 2015.

Charles Armstrong-Jones, Viscount Linley: Charles Patrick Inigo Armstrong-Jones, Viscount Linley (born 1 July 1999) is the only son of David Armstrong-Jones, 2nd Earl of Snowdon, and Serena Armstrong-Jones, Countess of Snowdon.  He is a great-grandson of King George VI.  He is heir apparent to the Earldom of Snowdon and 19th in line of succession to the British throne, after his father.

Robert Aagaard: Robert Aagaard OBE JP ( ; 27 June 1932 – 1 April 2001) was an English furniture maker and conservator, magistrate, and founder of the youth movement Cathedral Camps.

Eliphalet Chapin: Eliphalet Chapin (1741–1807) was a cabinetmaker and furniture maker in East Windsor, Connecticut in the late 18th century.  His style of furniture design is regarded as one of the most elegant of its time.

John McLean (furniture maker): John McLean (born 1770; died 1825) was an English furniture maker and designer.  He was recognized as one of the best of his era, representing the best in English cabinetmaking.  Examples of his furniture can be found in the Victorian and Albert Museum, The California Palace of the Legion of Honor and the Library at Saltram, Devon.

Lady Margarita Armstrong-Jones: Lady Margarita Elizabeth Rose Alleyne Armstrong-Jones (born 14 May 2002) is the only daughter and youngest child of the Earl and Countess of Snowdon.  She is the only granddaughter of Princess Margaret and the first of three granddaughters of the 1st Earl of Snowdon.

Thomas Sheraton: Thomas Sheraton (1751 – 22 October 1806) was a furniture designer, one of the "big three" English furniture makers of the 18th century, along with Thomas Chippendale and George Hepplewhite.  Sheraton gave his name to a style of furniture characterized by a feminine refinement of late Georgian styles and became the most powerful source of inspiration behind the furniture of the late 18th century.

David Armstrong-Jones, 2nd Earl of Snowdon: David Albert Charles Armstrong-Jones, 2nd Earl of Snowdon (born 3 November 1961), styled as Viscount Linley until 2017 and known professionally as David Linley, is an English furniture maker and the former chairman of the auction house Christie's UK.  The son of Princess Margaret, Countess of Snowdon, and of Antony Armstrong-Jones, 1st Earl of Snowdon, he is a grandson of King George VI and is 18th in line of succession to the British throne, the first in line who is not a descendant of Queen Elizabeth II.

Supporting paragraphs: Lady Margarita Armstrong-Jones David Armstrong-Jones, 2nd Earl of Snowdon
Answer: the British throne