Sadly not, it is the 0712 from Eastbourne to London Bridge, the last of the three direct trains.
Apparently there will be many more direct trains from Brighton to London Bridge, which is great, but as I don't live there it isn't so helpful to me.
So, I have the choice of changing trains, spending an hour longer at work, or stop commuting. The last of those seems the most attractive option right now.
I know there is a possibility that more trains will be added, but the ones uploaded to date match the exact pattern in the consultation proposal, so I'm not expecting miracles...