The announcement came in the company’s most recent financial results, which reveal that turnover rose to £14.4m in the year to August 2018, up from £11.7m in the previous 12 months.
But pre-tax profits fell to £322,600, down from £456,000 in 2016-17.
The company did not open any new sites during the period after witnessing “other restaurant operators struggling in the sector”.
Flat Iron has since launched two further sites in London Bridge and King’s Cross, which it says are both trading "ahead of expectations", and is now planning an additional opening, which is understood to be in the Spitalfields area.
The group’s managing director Jo Fleet told Restaurant magazine and MCA’s Generation Next event earlier this year that there was “no number” on the scale of restaurants the brand could open, but admitted there was no longer any appetite in the industry to reach 100 or 200 locations.
Flat Iron launched its first permanent restaurant in Soho in 2012 and now has seven London sites.