The City of London Livery Companies began as trade associations or trade guilds, which controlled who could carry out certain jobs in the City of London.

The Companies today 

Today the companies act mainly as social and charitable groups, because over the centuries the livery companies have lost most rights to control trade, often as statute law applied the same standards across the whole country.    Some support schools which were set up in the 1500s.  Others sponsor apprentices in colleges and unversities.  Some still have a statutory role.  For example the Goldsmiths' Company continue to run the London Assay Office where several million articles of gold, silver and platinum are hallmarked each year.

List of Companies in order of precedence 

The order of precedence was first set down in 1515 by the Aldermen of the City of London.  Forty-eight livery companies then existed.  The list was based on the companies' economic or political power.

The first twelve livery companies are known as the Great Twelve City Livery Companies. There are now 108 livery companies, some very new, so the Order of Precedence is sometimes reviewed.

The Merchant Taylors and the Skinners have always disputed their precedence, so once a year (at Easter) they exchange sixth and seventh place. This is one of the theories for the origin of the phrase "at sixes and sevens", as the master of the Merchant Taylors has said a number of times, although the first use of the phrase may have been before the Taylors and the Skinners decided to alternate their position. Both companies had been founded before the birth of Chaucer, who was one of the first people to use the phrase, so it may have dated from before him.

The Worshipful Company of Mercers (General merchants)
The Worshipful Company of Grocers 
The Worshipful Company of Drapers (Wool and cloth merchants)
The Worshipful Company of Fishmongers
The Worshipful Company of Goldsmiths
The Worshipful Company of Merchant Taylors (Tailors) (alternates with the Skinners)
The Worshipful Company of Skinners (Fur traders) (alternates with the Merchant Taylors)
The Worshipful Company of Haberdashers
The Worshipful Company of Salters
The Worshipful Company of Ironmongers
The Worshipful Company of Vintners (Wine merchants) 
The Worshipful Company of Clothworkers
The Worshipful Company of Dyers
The Worshipful Company of Brewers
The Worshipful Company of Leathersellers
The Worshipful Company of Pewterers
The Worshipful Company of Barbers (Barbers, surgeons, and dentists)
The Worshipful Company of Cutlers
The Worshipful Company of Bakers
The Worshipful Company of Wax Chandlers 
The Worshipful Company of Tallow Chandlers 
The Worshipful Company of Armourers and Brasiers (Armour makers and brass workers)
The Worshipful Company of Girdlers (Sword-belt and dress-belt makers)
The Worshipful Company of Butchers
The Worshipful Company of Saddlers
The Worshipful Company of Carpenters
The Worshipful Company of Cordwainers (Fine leather workers)
The Worshipful Company of Painter-Stainers
The Worshipful Company of Curriers (Tanned leather dressers)
The Worshipful Company of Masons
The Worshipful Company of Plumbers
The Worshipful Company of Innholders
The Worshipful Company of Founders (Metalworkers)
The Worshipful Company of Poulters
The Worshipful Company of Cooks
The Worshipful Company of Coopers (Barrel makers)
The Worshipful Company of Tylers and Bricklayers 
The Worshipful Company of Bowyers (Longbow makers)
The Worshipful Company of Fletchers (Arrow makers)
The Worshipful Company of Blacksmiths
The Worshipful Company of Joiners and Ceilers (Wood craftsmen)
The Worshipful Company of Weavers
The Worshipful Company of Woolmen
The Worshipful Company of Scriveners (Court document writers and notaries public)
The Worshipful Company of Fruiterers
The Worshipful Company of Plaisterers (Plasterers)
The Worshipful Company of Stationers and Newspaper Makers
The Worshipful Company of Broderers (Embroiders)
The Worshipful Company of Upholders (Upholsterers)
The Worshipful Company of Musicians
The Worshipful Company of Turners (Lathe operators)
The Worshipful Company of Basketmakers
The Worshipful Company of Glaziers and Painters of Glass
The Worshipful Company of Horners
The Worshipful Company of Farriers (Horseshoe makers and veterinary surgeons for horses)
The Worshipful Company of Paviors (Road and highway pavers)
The Worshipful Company of Loriners (Harness makers)
The Worshipful Society of Apothecaries (Medical practitioners and pharmacists)
The Worshipful Company of Shipwrights
The Worshipful Company of Spectacle Makers
The Worshipful Company of Clockmakers
The Worshipful Company of Glovers
The Worshipful Company of Feltmakers (Hat makers)
The Worshipful Company of Framework Knitters
The Worshipful Company of Needlemakers
The Worshipful Company of Gardeners
The Worshipful Company of Tin Plate Workers
The Worshipful Company of Wheelwrights
The Worshipful Company of Distillers
The Worshipful Company of Pattenmakers (Wooden shoe makers)
The Worshipful Company of Glass Sellers
The Worshipful Company of Coachmakers and Coach Harness Makers
The Worshipful Company of Gunmakers
The Worshipful Company of Gold and Silver Wyre Drawers 
The Worshipful Company of Makers of Playing Cards
The Worshipful Company of Fanmakers
The Worshipful Company of Carmen
The Honourable Company of Master Mariners (first of the 20th century companies)
The City of London Solicitors' Company
The Worshipful Company of Farmers
The Guild of Air Pilots and Air Navigators
The Worshipful Company of Tobacco Pipe Makers and Tobacco Blenders
The Worshipful Company of Furniture Makers
The Worshipful Company of Scientific Instrument Makers
The Worshipful Company of Chartered Surveyors
The Worshipful Company of Chartered Accountants in England and Wales
The Worshipful Company of Chartered Secretaries and Administrators
The Worshipful Company of Builders Merchants
The Worshipful Company of Launderers
The Worshipful Company of Marketors
The Worshipful Company of Actuaries
The Worshipful Company of Insurers
The Worshipful Company of Arbitrators
The Worshipful Company of Engineers
The Worshipful Company of Fuellers
The Worshipful Company of Lightmongers
The Worshipful Company of Environmental Cleaners
The Worshipful Company of Chartered Architects
The Worshipful Company of Constructors
The Worshipful Company of Information Technologists
The Worshipful Company of World Traders
The Worshipful Company of Water Conservators
The Worshipful Company of Firefighters
The Worshipful Company of Hackney Carriage Drivers (Taxi drivers)
The Worshipful Company of Management Consultants
The Worshipful Company of International Bankers
The Worshipful Company of Tax Advisers
The Worshipful Company of Security Professionals

Two old companies do not intend applying for a grant of the right to wear the special costume or uniform known as a livery.

The Worshipful Company of Parish Clerks
The Company of Watermen and Lightermen

Three groups intend applying for livery.  One has already been recognised as a "Company without Livery" the other two have not yet existed long enough or become well enough known.

The Guild of Public Relations Practitioners
The Guild of Arts Scholars, Dealers & Collectors
The Company of Educators

References

Trade
London