Fair enough, I agree the situation is mildly infuriating, whatever the reason you wanted it. A lot of restaurant/pub chains over here will throw out extra food if they prepped too much, rather than letting staff take it, probably because they don’t want people creating waste on purpose but also don’t want to spend the minimal effort required to stop people abusing the system if they allowed people to take excess food home. The distrust of low paid workers leads to most stores being unable to deal with special requests unless you are speaking to the manager and I don’t know where I’m going with this…
*Curries unless you’re talking about the electronics retailer
If you’re just referring to the restaurants, I’d just call one of those restaurants an Indian (as in the cuisine) or maybe a curry house. Tandoori, Balti, etc. all relate to styles of cooking and may be used in restaurant names, but if I was referring to restaurants that serve Indian style curries in general, I would just call it an Indian.