Dear Atria, I don't know if you and/or your mother are aware of an existence of Azerbaijan Airlines (AA), so I wanted to recommend this airline to you as they offer exceptional service and are very good value for money as well. I am not in any way connected with this airline and I don't have any interest in it. I am just a happy customer who wants to share his experience and recommend service I received.
The only disadvantage of flying with AA (for some people - for me it didn't matter) could be that there is no direct flight from London to Tehran. You have to change in Baku (Azerbaijan). The flight from London Heathrow to Baku takes about 5 hours 30 minutes (that's the one with Boeing) and then the flight from Baku to Tehran is only 45-60 minutes (it is with the small plane, but also modern and comfortable and even on that short flight they serve tea and coffee). I didn't have to wait long in Baku on my way to Tehran, I think it was just about over an hour, which was enough to go through security etc. On my way back I had a longer stay in Baku - few hours, but again, it wasn't bad. The Heydar Aliyev airport in Baku is very modern (the terminal was built for the Olympics last year), comfortable and I also found couple of other people who were waiting for their flights, so we spent all the time chatting, had something to eat and we just entertained ourselves. All in all I can certainly recommend Azerbaijan Airline, so check it out for your next travel to Iran :-)