The closures will impact 120 staff, although the company will attempt to place those affected in other parts of Oliver's restaurant empire.
Restaurants in Aberdeen, Cheltenham, Exeter, Ludgate, Richmond (both in London) and Tunbridge Wells are all scheduled to close in the first quarter, the Jamie Oliver Restaurant Group said today.
Chief executive Simon Blagden said: "As every restaurant owner knows, this is a tough market and, post-Brexit, the pressures and unknowns have made it even harder.
"While our overall business is in very good shape - we finished last year with like-for-like sales growth and an increase in covers - because we refuse to compromise on the quality and provenance of our ingredients and our commitment to training and developing our staff, we need restaurants that can serve an average of 3,000 covers every week to be sustainable."
As well as staff costs and lower footfall, the group has been stung by the collapse in the pound, which has ramped up the cost of buying ingredients from Italy.
According to accounts filed at Companies House, revenue at Jamie's Italian rose by almost 9 per cent to £116.1 million in 2015, although profits fell from £3.8 million to £2.3 million.
There are 42 Jamie's Italian outlets in the UK and 28 overseas.
It employs 3,100 in Britain, and Mr Blagden added: "These closures are in no way a reflection on the dedication and commitment of our staff and my first priority is to try and secure those affected alternative jobs within other Jamie's Italian restaurants.
"Where this isn't possible, we'll be working with them to find alternative employment. Jamie's Italian has become a much loved presence on the UK high street and we have our teams to thank for that. These closures represent less than 5% of total turnover and impact less than 5 per cent of our team members."
The group said it will now focus on the "core Jamie's Italian estate" and on the expansion of the Barbecoa brand, which will see two new openings in 2017.
Internationally, the firm plans to launch another 22 Jamie's Italian restaurants and develop its newly acquired Australian restaurants.