These labels are now worldwide multi-million-dollar, empires, seen on everything from perfume to handbags to shoes in their efforts to outflank their rivals. Yet the name of each company is the same as that of the family behind the label, and their struggle to come out on top of all the others would be familiar to any student of Italian medieval history - for Prada and Gucci, you could read Montague and Capulet. All are based in Milan which, beneath its glitzy veneer, is a typical small Italian town where dynasties and family allegiances run deep.
Even in August, traditionally the month when the fashion industry shuts up shop and heads for the coast, Prada was setting its sights on world domination. Last week the group, with sales of more than $1bn (pounds 625m) and stores across the globe, entered the genteel world of traditional British shoe-making by taking an 8.5 per cent stake in Church & Co, purveyor of footwear to the Prince of Wales. It was also reported that the company was moving in on Jil Sander, Germany's most aspirational designer tag, paying $109m (pounds 68m) for a 52 per cent stake. (Sander herself denied any such claim.)
Prada's interest in Church's is just the latest in a series of acquisitions which began last summer, when the company discreetly amassed a 9.5 stake in arch-rival Gucci. It later sold that stake on to French luxury goods conglomerate Louis Vuitton/Moet Hennessey (LVMH ) for a $120m (pounds 75m) profit, the proceeds of which went towards forming an alliance with Austrian-born uber-designer, Helmut Lang.
The family nature of the business can be seen in the Milan mansion of Miuccia Prada and her husband Patrizio Bertelli, where, despite the expensive contemporary art on the walls, children charge noisily about. But the couple are acquiring a reputation as the most ferociously motivated business people in world fashion. Bertelli, the business brains behind the Prada dynasty, is said to control the running of the company to the point where he monitors the distance between phones and keyboards on employees' desks. For her part, Miuccia oversees the design of Prada as well as the younger Miu Miu line and is the all-important front person for both labels.
Like Armani and Versace before them, Prada and Gucci could not be more different. When American designer Tom Ford took the helm of Gucci in 1995, he created the rock chick's label of choice. Gucci is overtly sexy, supremely glamorous and screamingly expensive - the label favoured by "It Girls" the world over.
Prada demonstrates a more dowdy aesthetic: discreet luxury, often subtly embellished with arts and crafts finishing, aimed at a woman who would rather not wear her wealth on her sleeve but is just as monied as her more flashy Gucci sister. Both, however, are equally influential: the British high street would be in a sorry state were it not for the Gucci and/or Prada spin-offs that fill the rails from Warehouse to Marks & Spencer.
Just like LVMH, whose chairman, Bernard Arnault, is regarded as the Rupert Murdoch of fashion, Prada is continually broadening its interests. The husband-and-wife team have put money into contemporary art through the Prada Foundation in Milan's affluent Via Spartaco. Bertelli is also keenly involved with Luna Rossa, the Prada yacht, currently heading towards New Zealand and January's Americas Cup. Prada has invested $40m (pounds 25m)in the challenge, which would be amply repaid if it won, through publicity for its already hugely successful Prada Sport line, worn by all Luna Rossa crew members.
The Prada label has come a long way since Miuccia's grandfather started out making leather shoes and belts in the provincial village of Levanelle, near Arezzo, in 1913. In typical Italian dynasty style, the production core of the company is still based there. In March the construction of a 60,000 square metre building to make room for a further 150 members of staff was announced.
Miuccia herself began designing accessories for the house in the late Seventies, having completed a degree in politics and a brief spell working for Italy's Communist Party. By the beginning of the Nineties the Prada bag, crafted in simple black nylon but boasting the discreet Prada logo etched on to a black metal triangle, was a must-have from the streets of Manhattan to the beaches of Rimini, where a nice line in fakes continues to sell like hot cakes to this day.
A small but perfectly formed clothing line, first for women, then men, followed. Prada is now worn by everyone from Nicole Kidman and Sigourney Weaver to Meg Matthews and Patsy Kensit. On a less obviously glamorous note, the company also provided the suits for the all-conquering Manchester United team earlier this year.