Yes indeed, one of the key output strategies is to run trains from Brighton (etc) to Peterborough - but don't hold your breath, it's not due until 2015 !!
If you've been down to St Pancras International Low Level, at the Country End you'll have seen the two tunnel mouths for the ECML links. IIRC they come up somewhere north of the Grand Union - possibly here...
http://www.flashearth.com/?lat=51.53....8&r=0&src=msl
Whilst we're speaking of the Thameslink project, the Sevenoaks route is about to be invaded by 319 units later this month when at last trains run through to St Albans, Luton & Bedford.
Just like the old days, ho hum.