In the mid 90s, MTL (of Merseyside) bought a coach company in Morecambe, Heysham Travel, and ran services in competition with the main operators as a cheap, low cost fleet. According to Wikipedia, it was originally planned to be a springboard to get a foot in the door into buying Lancaster City Transport (LCT), but Stagecoach got LCT instead during the "bus wars". However, MTL kept the bus operation going until MTL itself was sold to Arriva.
I'm not sure if this example counts, but Heysham Travel when it ran was very much a "low cost" operation. The tickets were cheaper than Stagecoach and the buses were clapped out run-down offcasts (much worse than in the core Merseyside operation). When I was younger and lived that way I used them a couple of times, but whereas Stagecoach would run every 20 minutes, Heysham Travel would be hourly - if they bothered to turn up at all. For that reason getting a return ticket would be pointless. I don't remember now if they did tendered routes but they certainly did some commercial routes, although I never really saw the point. It seemed more like a "we've got a bus, let's run it somewhere" type operation.
However, if I remember right, despite the external branding as "Heysham Travel", the actual licensing wording on the side of the buses was MTL Holdings Limited.