In total, 9.5m sq ft is under construction, with nearly half of all development located in the City, where several new skyscrapers are under way.
Property developers are responding to rising corporate demand from businesses since Britain’s economy returned to growth, the research showed.
In particular, the increase in occupier demand came from technology and creative sectors, which comprised half of all new lettings in the period.
Little new space was built in central London in the five years after the financial crisis, meaning that occupiers now face a supply shortage.
Due to strong tenant demand, the City has the lowest proportion of space under construction that is available to let of any area in central London.
Just half is unlet, compared with 84 per cent in the West End and 59 per cent in the Docklands, according to Deloitte.
The amount of office space available in the City is at its lowest level for more than a decade, separate figures from property adviser DTZ showed. As a result, rents in the area have risen 14 per cent in the past two years.

Anthony Duggan, head of real estate strategy at Deloitte, said: “We are now seeing the start of the supply response the market has been expecting, thanks to the robust economic conditions strength of London as a global city.”
Sophy Moffat, a senior analyst at DTZ, said the market was likely to see “pronounced rental growth” with the cost of the highest-quality buildings experiencing “double-digit rises”.
Mr Duggan predicted that the market would see “further rises in rents and more pre-let deals on schemes under construction as tenants compete for the limited amount of available space.

Canadian property investor Brookfield is building a rival tower just a few doors up the street.
US financial giant TIAA-CREF has plans for a set of chunky, slab-style office buildings further to the south, dubbed Gotham City.
And next door to the City’s most popular tower, the Gherkin, global insurance company WR Berkley is building a new high-rise headquarters for itself, nicknamed the Scalpel.