Coming from the south a London Terminals ticket is in fact valid as
far as City Thameslink.
At Blackfriars, despite it being gated, there should be Oyster readers
somewhere on the platform - perhaps near the subway - so passengers
transferring from Southeastern trains on a rail-only ticket can touch-
in their Oyster and thus continue travelling northwards on the
Thameslink route without needing to exit and re-enter the gates. You
could thus get off at Blackfriars and try and do this, perhaps even
getting back on the same train.
Don't go to Victoria as the Victoria line is closed all day sunday.
The number 4 bus goes from outside City Thameslink to up to the Angel,
Islington - see this PDF of the Ludgate Circus bus spider map:
http://www.tfl.gov.uk/tfl/gettingaround/maps/buses/pdf/blackfriarsandludgatecircus...
If you do this you'd need to ensure you leave City Thameslink station
by the southern Ludgate Hill exit. There isn't much traffic in the
City at the weekend so this might well be a quick route to take.
Otherwise you should be able to buy an extension ticket at Brighton so
you could stay on the Thameslink train and transfer to the Northern
line at KX. The Thameslink line through central London can be treated
as if it were part of the Underground network, so a U1 (i.e.
Underground zone 1) ticket would be good for the whole Thameslink +
Tube journey, and you should be able to buy this from the ticket
office in Brighton.
