Personally, I see Thomsonfly going following a very similar business model to that of our German partner airline Hapagfly. This company has a built up a network of "mini hubs" across Germany with multiple weekly flights to holiday destinations across Europe, attracting both their own pax with a no-frills airline pricing structure but also pax who are connecting to a group-owned holiday company. The airline uses a fleet of 737-800s which are the perfect size for the operation; allowing fast turnarounds & being ideal for the number of weekly flights they operate. There is also a dedicated LCC division (HLX) which operates scheduled flights from markets they've been able to get a toehold in with slightly smaller planes but increased frequencies, which seems to fit in with TOM's CVT/DSA/BOH operation.
The BritanniaFly rumour is sentimental rubbish. TUI have just spent a lot of money in promoting the Thomsonfly brand, and introducing the Thomson brand to all aspects of the TUI UK products. I can't see them disbanding now. As lovely & respected the BY brand was to those in the know, it's known predominantly as a "charter" brand, therefore a fresh new look as the airline approaches a new business model is what's needed.