You can find a big guide to Budapest shopping here.
All stores were open on Sundays for many years until the politicians decided to close them. This remained so for a couple of years before they removed the law, meaning that stores can now stay open on Sundays if they want to. As a result, most stores are open on Sundays, though some are open for a shorter period than on the other days of the week. As a result, many grocery stores close around 18.00 on Sundays (instead of 20.00 or 21.00 or 22.00), but some exceptions stay open for a longer time.
Special stores with private owners keep open based on the command of their owners. Some keep open on Sundays while other’s don’t. Fashion stores in the shopping street Vaci utca and in the malls are all open on Sundays.