Not sure how it was launched, but London Transport (the predecessor to TfL) would not have had a role because it was strictly a BR project.
London Transport didn't have a role but it was something with original involvement from the Greater London Council.
Initial routes were, in order through the Core, across an off-peak hour in 1989:
* Bedford to Gatwick Airport via London Bridge
* Cricklewood to Sevenoaks via Catford / Petts Wood
* Luton to Purley via Streatham
* Bedford to Brighton via London Bridge
* Cricklewood to Sevenoaks via Catford / Bat & Ball
* Luton to Purley via Streatham
At peak times, there were only four trains an hour through the core with the Luton trains diverted to the Wimbledon loop and the Gatwick / Brighton trains diverted via Tulse Hill. There were no peak trains to Sevenoaks. This was to provide sufficient numbers of the 319 fleet on the Midland route.
Later, the Sevenoaks trains were all diverted to the Bat & Ball route, Gatwick trains extended to Brighton and the Purley trains went instead to Guildford off-peak via Streatham and West Croydon and the Wimbledon / Sutton loop in the peak. The Guildford service was subsequently cut back to West Croydon.
Finally, Thameslink took over the Wimbledon / Sutton loop completely prior to privatisation, pulling out of the West Croydon route and off-peak Bedford to Gatwick / Brighton services went 4tph.
There clearly were grandiose plans for Thameslink 2000 which I don't have to hand but think I do have a supplement from Rail somewhere which describes what was planned.