Those DornierJets are very unusual; there are only a handful left in commercial service around the world.
They're operated by Sun-Air of Scandinavia, based in Billund, who are the only remaining BA franchise partner. They operate under the BA brand, and used to operate scheduled flights from London City and Manchester to Billund under a BA flight number until last month; see
this Flyertalk thread. You used to be able to book these on the BA website - including as Avios redemptions, which were exceptional value given the cash fares.
Sun-Air have their own service standards, and although their aircraft are in an all-economy layout they effectively provide everyone with a business class service - and charge accordingly for the privilege!
Unfortunately it appears they have now ceased operating scheduled flights, so it's just charter flights left now. I'm glad I flew with them while I had the chance - the service was exceptional; there was only 1 other passenger on the flight I took - though they were very difficult about paying EU261 compensation.