The property firm said there will be a 30-40 per cent drop in development activity in 2017, with London being hit particularly hard.
The drop-off in property development will peak in 2019-21, pushing up rents as the capital runs out of space in highly-prized offices.
The gloomy outlook from Savills comes after the City's biggest tower, 1 Undershaft, won planning permission. The 73-storey tower will house around 10,000 City workers, and goes some way to providing space for the 50,000 extra workers the City of London Corporation is expecting to arrive over the next 30 years.
International investors will be looking beyond the capital for investments - a trend that has already been observed by regional property firm Sirius Real Estate.
"Non-domestic investor interest in the UK will continue to rise, with the next five years likely to see record levels of international investment in assets outside London," Savills said.
Demand for space outside London will remain high as firms continue to relocate staff to regional cities, but, due to the lack high quality office spaces in these areas, competition will be fierce.
Mark Ridley, chief executive of Savills UK and Europe, said:
'Expect the unexpected' is now the normality, not the exception, on the world stage. Despite this, property remains a fundamentally safe asset class, giving strong income returns and, in many cases, is a refuge for capital preservation in the longer term, its appeal remaining resolute.
Savills also said that the residential property market will slow in the coming years, with transaction volumes falling 16 per cent over the next two years. But international investors will be lured into London by sterling's slide since the Brexit vote.
Ridley said: "The sterling devaluation has made UK property very attractive for international investors pegged to the US dollar or euro, with 2017 activity in central London likely to be dominated by Asian investors, with American and European investors also strong nationally."