I do not recall British department stores ever shutting down for lunch. Indeed, in the '70s many of them would (some still do) contain restaurants, inside the store, open to the general public to have lunch in, so they had to be open for that.
On the other hand, 9 or 9.30am opening to 5.30 closing is quite realistic. That was standard for most British shops in the '70s and is still quite common (give or take a half hour or so at either end) today, although small supermarkets mostly seem to stay open now until about 9pm, and larger ones until midnight, or even stay open 24 hours.
There was also, back then, “early closing day” mandated by law, where, one day a week, almost all the shops in a certain area would close down for one afternoon a week (which day varied by town or district I think). Hardly any shops opened on Sundays, either, again, regulated by law. Early closing day has gone, now, and some shops (far from all) do open on a Sunday, though usually for fewer hours than on weekdays. Certainly shopping hours still remain a lot more restricted in Britain than in cities in the United States.
The “old” British shopping hours, which still prevailed in the 1970s, must have made it very difficult for people with jobs with regular hours to shop. Shop hours basically corresponded to regular working hours. I believe the lunch hour (and Saturday) often became a shop’s busiest time, but the whole system, back then, was presumably still geared to an era when most women did the family shopping, and did not have jobs outside the home. Of course, even by the 1970s, that was no longer really true.
Mind you, even if Are You Being Served is nominally set in the 1970s, the world, social attitudes, and the sort of shop, it represents (in caricature form) always seems to me to be more like the 1950s, or even earlier. Places Grace Brothers, in the '70, were already very old fashioned and dieing out (and, of course, its old-fashionedness is exaggerated for comic effect).
