The body, which represents more than 370 councils in England, believes that failure to comply should result in either a fine or prosecution.
Council environmental health teams score outlets from zero to five based on factors such as kitchen cleanliness, cooking methods and food management.
However, in England, businesses do not have to display the ‘Scores on the Doors' rating they have been awarded.
Councillor Simon Blackburn, chair of the LGA's safer and stronger communities board, said: "Forcing all food outlets in England to display a hygiene rating would help to crack down on and expose businesses that flout the law and put people at risk by incentivising them to improve or maintain high hygiene standards and show customers how seriously they take the issue.
"A good food hygiene rating is good for business and people in England should also now be able to use it to decide if they are happy with their choice of food outlet, or would prefer to go somewhere else with higher standards.
"With mandatory hygiene rating display already in force in Wales and becoming law in Northern Ireland this year, it is time the legislation was extended to England as well."
An FSA spokesperson said: “We very much favour making it compulsory in England too as we believe this will be better for consumers. It will also be better for businesses that achieve good standards as they will get more recognition and it will increase the spotlight on those not meeting the grade.
“We have been monitoring the impact of mandatory display in Wales and using evidence from this to build the case for introducing a similar requirement in England. We are also exploring how a statutory scheme could be delivered in England within the context of reducing local government resources. It is anticipated that proposals will be presented to the Government by the end of the year.”