The chef will close sites in Exeter, Aberdeen, Cheltenham, Richmond, Ludgate Hill and Tunbridge Wells by the end of the first quarter of the year.
The move will affect 120 employees, though Oliver said he hopes to find the workers alternative jobs.
Simon Blagden, chief executive of the Jamie Oliver Restaurant Group, told The Guardian that the rising cost of ingredients and staff training had impacted the decision.
However, he added that the 42-strong Jamie’s Italian group was ‘in very good shape’ overall.
It follows warnings from suppliers that food and drink prices could rise by as much as 11 per cent post-Brexit.
The Wine and Spirit Trade Association (WSTA) said last year that the weakened pound could see the price of a bottle of wine increase by an average of 29p.
“As every restaurant owner knows, this is a tough market and post-Brexit the pressures and unknowns have made it even harder,” said Blagden.
The announcement follows Oliver’s decision to take over the six-strong Australian-based Jamie’s Italian chain after its franchisee Keystone Group went in to receivership last year.
Oliver operates over 25 restaurants internationally alongside his 42 UK sites.