Sheffield City Council say the owner of Cake 'R' Us, in Devonshire Street, did not have consent for the work.
It says the shop must be repainted in a colour scheme "more in keeping with its 19th Century characteristics".
Owner David Chan said he had painted the shop in an "act of national pride".
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A complaint about the shop, which is in part of the former Wharncliffe Fireclay Works built for John Armitage in 1888, was received in January 2015.
The council wrote to Mr Chan to say the design was "unacceptable" but was told he had "no intention of repainting the shop" and would instead apply for consent. It said though no application has yet been made.
Mr Chan said: "It's the Union Jack. I do not see why it needs to be changed. I support Queen and country."
Asked what he would do if the council took legal action to make him repaint the shop he said: "I will write to the Queen. I do not see anything wrong with it. It's an act of national pride."
A council report said: "The union flag theme that has been applied to the shop front is considered to be visually intrusive and does not respect the original character of the property to which it is attached, due to its contemporary and garish design.
"Whilst the need of the business to advertise its presence and attract custom is recognised, this shop front has a deep fascia and projecting sign for these purposes, and there is no justification for garish and unsympathetic painting of the shop front to serve this purpose."
The report recommends that the council's planning committee, which is due to meet on 26 April, agree to take any "appropriate action including, if necessary, enforcement action and the institution of legal proceedings to secure repainting of the shop front".

The Spaniard, 34, won the Tour de France in 2007 and 2009, but he was stripped of the 2010 title for doping.
He is one of only six riders to have won all three Grand Tours - the Tour de France, Vuelta and Giro d'Italia.
"I don't think there is a better farewell than the home race in my home country," he said on Instragram.
Contador, who turned professional in 2003, added: "I'm saying this happy, I'm not saying it with sadness. It's a decision I've thought about very well."
He was banned for testing positive for clenbuterol - a powerful drug used to treat asthma, but which can also help build up lean muscle mass and burn off fat - at the 2010 Tour de France.
Contador blamed his positive test on eating contaminated steak.
The Court of Arbitration for Sport (Cas) banned Contador in February 2012, but backdated the ban to 25 January 2011.
Having served five months and 19 days of a provisional suspension in 2010-11, he returned to cycling in August 2012.
Contador won seven Grand Tour titles and was awarded the prestigious Velo d'Or, voted for by journalists, a record four times.
Only Eddy Merckx, Bernard Hinault, Jacques Anquetil, Felice Gimondi and Vincenzo Nibali have also won all three Grand Tours.
A man who painted the front of his Grade II listed shop with a "garish and unsympathetic" union flag is facing possible legal action for breaching planning regulations.
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Two-time Tour de France champion Alberto Contador is to retire from professional cycling after the Vuelta a Espana, which starts on 19 August.