In this case, various northbound Thameslink services aiming for the Midland Mainline (ie. St Albans/Luton/Bedford etc.) were held in the Core due to the incident on the MML. However, these stationary or slow moving trains were (bar one) on the westernmost of the two lines.
While they were being held, or terminated and moved out of the way, other Thameslink services which run via the East Coast Mainline (ie. Peterborough/Cambridge etc.) were sent on the adjacent line in the same direction, in order to overtake the trains which were being held.
The incident on the MML was such that all lines through the incident site were blocked for some time, so there were very few southbound trains which needed to be held for the northbound trains to run on both lines.
The signalling system is fully equipped to route trains onto either line through the Core section within Central London, and has been for years.