They had a weird reputation - a friend of mine was a flight engineer with them (727s; and loadmaster on the old Hs 748s) and I finally got the courage to ask him why they were such a laughing stock and he said he didn't know, but when he told people who he flew for, they did indeed laugh in his face.
Their safety record was pretty OK
, I think they lost a 727 in Tenerife in 1980 (ish) but they at one point had a fleet of 44 Comets, they did RTW charters with their 707s, and were Britain's first low-cost airline, paving the way for easyJet and Ryanair, and provided significantly better service than either do today. Pretty cool stuff. I don't know why the British public gave them such a hard time, they were a great meat-and-potatoes flying outfit, very dedicated and pro team. I also don't know why Dan Air didn't dump the name and shitty livery and rebrand themselves Britworld or something. When they tried to build up a sked operation in the late 80s and 90s, they just couldn't get the yield, they were still Dan Dare.
The (London) was so people didn't think they were Danish, Dan stood for Davies And Newman. Truth is they weren't really (London), they had planes and crews based all over the British Isles and indeed Germany. So the name was a complete mess. It's hard to miss an airline so unable to save itself, they persisted and everyone always knew it wasn't going to work out.
fly Saha Air 707s daily from Tehran's downtown Mehrabad to Mashhad, Kish Island and Ahwaz