Airfix was founded in 1939 by a Hungarian businessman Nicholas Kove, initially manufacturing rubber inflatable toys. The brand name Airfix was selected to be the first alphabetically in any toy catalogue. In 1947, Airfix introduced injection moulding, initially producing pocket combs.

In 1949, it was commissioned to create a promotional model of a Ferguson tractor. The model was initially moulded in cellulose acetate plastic and hand assembled for distribution to Ferguson sales representatives. To increase sales and lower productions costs, the model was sold in kit form by F. W. Woolworth's retail stores.

A few years later in 1954, Woolworth buyer Jim Russon suggested to Airfix that they produce a model kit of Sir Francis Drake's Golden Hind, then being sold in North America as a 'ship-in-a-bottle'. The kit would be made in the more stable polystyrene plastic. In order to meet Woolworth's retail price of 2 shillings, Airfix changed the packaging from a cardboard box to a plastic bag with a paper header which also included the instructions.

It was a huge success and led the company to produce new kit designs. The first aircraft kit was released in 1955, a model of the Supermarine Spitfire, in 1/72 scale. This was a scaled down copy of the Aurora 1/48 Supermarine Spitfire kit. Kove initially refused to believe the product would sell and threatened to charge the cost of the tooling to the designers.

During the 1960s and 1970s, the company expanded greatly as the kit modelling hobby grew enormously. The Airfix range expanded to include vintage and modern cars, motorcycles, figures, trains, trackside accessories, military vehicles, large classic ships, warships, liners, engines, rockets and spaceships, as well as an ever-increasing range of aircraft. Most kits were created at the "standard" scale of 1/72 for small and military aircraft, and 1/144 scale for airliners.

The 1963 acquisition of the intellectual property and 35 moulds of Rosebud Kitmaster gave Airfix their first true models of railway locomotives in both OO and HO scales as well as their first motorcycle kit in 1/16th scale - the Ariel Arrow.

Note: Most of Airfix's older range of military vehicles though originally packaged as 1/72 are generally accepted as actually being OO or 1/76 scale. The recent introduction of a small number of true 1/72 vehicle kits to the Airfix range meant that you couldn't be completely sure from just looking at the box what the true scale was. However, following Airfix's acquisition by Hornby this has been clarified as the kits are now being distributed in new packaging showing either 1/72 or 1/76 as appropriate.

In the mid 1970s, larger scales were introduced, including the dramatic 1/24 scale models of the Spitfire and Hurricane and Harrier "jump-jet", which featured unusually extensive detailing at this scale. All the kits were manufactured using injection moulding of polystyrene. They were categorised into Series from 1 to 20 depending on their size and complexity and were priced accordingly. The only Series 20 product was a 1/12 scale kit of the 1930 Supercharged Bentley 4.5 Litre car with 272 parts and the option of a 3 volt motor.

The growth of the hobby launched a number of competitors in the field, such as Matchbox, as well as introducing new manufacturers from Japan and the US to the UK. During this period the company Humbrol also grew, supplying the paints, brushes, glue and other accessories for the finishing of the kits.

In this period, apart from model kits, Airfix also produced a wide range of toys, games, dolls and art & craft products. Airfix Industries acquired the Meccano and Dinky Toy businesses in 1971.

Airfix also launched a monthly modelling magazine, Airfix Magazine, which was produced by a variety of publishers from June 1960 to October 1993. During the 1970s, an Airfix Magazine Annual was also produced and Airfix books were published by Patrick Stephens Ltd on classic aircraft, classic ships and modelling techniques.

In the 1980s, the plastic kit modelling hobby went into a rapid decline. Some think this was due to the rise of computer games, others that new manufacturing techniques such as precision diecasting took away the market for toys, where a person was less interested in the construction and finishing of a model, but simply wanted to play with the finished product, others the declining birth rates leading into smaller generations and declining numbers of potential enthusiasts.