Its 1,000 Companies To Inspire Britain report found firms are expanding at an average of 50% a year, and that 78% of the most rapidly growing firms are based outside the English capital.
Scottish companies are fastest growing with 83% annual average revenue growth, according to the analysis.
Outside London, Greater Manchester is the top area as home to 36 companies with Leeds and Aberdeen next on 16 each.
Wales and Northern Ireland's small and medium sized enterprises have grown by 25 since last year, according to the annual report.
Xavier Rolet, chief executive of the London Stock Exchange Group, said: "High growth SMEs are the driving force behind the UK economy, developing the skills, jobs and growth we need.
"But ambition alone is not enough; their success must be highlighted and their growth properly supported with appropriate finance.
"That's why today's event is so important: demonstrating the strong alliance between UK Government, financial market participants, investors, entrepreneurs and companies to support these inspiring businesses.
"Today's celebration is fundamental to London Stock Exchange's core, the need to support UK high growth companies in their journeys from start-up to stardom and create an entrepreneurship revolution."
Around a quarter of the firms are from the construction, engineering and manufacturing sectors and there has been a 17% increase in food and drink companies, according to the report.
Just 13.5% of the directors across the 1,000 firms were women, it found.
The information technology sector was the top performing sector, enjoying 350% growth between 2010-14.
Some 147 companies made the list again following last year's report, with Metro Bank seeing a 171% increase in revenues.
The report features 217 companies from Greater London, 148 from the South East, 101 from the North West, 89 from East of England, 80 from the West Midlands, 79 from Yorkshire and The Humber, 56 from Scotland, 36 from Greater Manchester and 29 from Lancashire.
Chancellor George Osborne said: "UK high-growth businesses are leading the charge in rebuilding our economy. These companies are the backbone of the British economy.
"They create high-quality, well paid jobs, innovate and drive economic growth. This Government fully understands the need to support ambitious entrepreneurs and ensure they can access the finance they need to grow.
"We have held the steadfast belief that - alongside deficit reduction - nurturing entrepreneurs, creating jobs, supporting hard-working families and keeping taxes low would get the UK economy back on track.
"Our measures to increase access to finance for business and encourage more investment have had a transformative effect on our economy."
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