Four new restaurant sites are expected in the next five years, initially in London locations such as Soho, London Bridge and St Pancras. Two new London sites have already been agreed - with one on Endell St, near the existing restaurant, and another expected for the Farringdon area (the exact location is yet to be announced).
The company also announced potential plans for new sites in Manchester and Birmingham, and added that it had considered opening in the Middle East.
Managed by brothers Ahmet and Ali Ziyaeddin, the original Covent Garden site has been owned by the same family for more than 35 years, and has now secured funding from a number of investors, thanks to a partnership with BGB Capital Partners.
The current site combines both a restaurant and a takeaway in one place, but the new expansion drive will separate these two operations, with the first named the "Rock and Sole Plaice Kitchen", and the second a takeaway "RSP express" concept.
The restaurant brand will focus on 60-80 seat spaces, with a bar serving a wide variety of drinks including craft beers in bottle and on tap. The second will be a quick-service operation focusing on the takeaway side of the business, positioned in high-footfall locations in cities and in stations.
For the restaurant, average spend is expected to be at £15-18 per head, while the takeaway operation will charge significantly less, in a bid to entice passing trade.
The interior décor of both brands' new sites is expected to emphasise the original business' history, and create a modern yet traditional feel.
Ahmet Ziyaeddin stated that he was excited about the move, as he felt fish and chips were making a "strong statement in the market".
He said: "We are [well-placed] to expand… already having the infrastructure of a centralised kitchen in place. Our passion for the product, coupled with its heritage, means that we will be able to grow throughout the good and the bad times."
His brother Ali added: "We have identified our second site and are looking at many different locations for further expansion, where you can find accessible premium brands."
The original site was the only fish and chip restaurant to be named by Alain Ducasse in his recent city-based food guide "J'aime London". It serves classic fish and chip dishes using fish such as haddock, halibut, rock, sole and plaice.