The figure is a four-year high and up 8% over the last six months.
Figures in the latest London Crane Survey by Deloitte Real Estate reveal construction activity across the capital has more than trebled since hitting a low in mid-2010.
Tenants have also been agreeing more leases on new space.
In Q1 2013, 33% of space under construction was pre-let – the equivalent to six Shards.
That is a sharp contrast to 2011 when only 1% was pre-let.
Nearly 4.5 million sq ft is currently under construction in the City of London – up 10% since the last survey in November.
Anthony Duggan, partner and head of research at Deloitte Real Estate, said: “The increase in construction and leasing transactions recorded in the latest survey reflects the improving sentiment being felt in the London office market.
“Importantly, a number of the ‘bellwether’ vacant schemes across London are now transacting, reducing the ability of potential occupiers to sit back and wait for conditions to improve.
“This is likely to add a little more urgency into the leasing market over the next few months.”