In the past the Thameslink route didn't exist. Trains coming from South London would run into a terminus at Holborn Viaduct (Holborn Viaduct Station) whilst trains serving local North London stations terminated at St Pancras station.
The Metropolitan Underground Railway is full of disused feactures. One of these feactures was the disused Snow Hill Tunnel. The Snow Hill tunnel used to run from around High Holborn through the old Kings Cross Metropolitian railway station and most probably to sidings above ground. This cut-and-cover tunnel lay disused until the 1990s when the Thameslink Project sought to link both North and South London.
The extension included the use of the old (~50 year old) tunnel again. The work included refurbishing the link to Farringdon Station's old Met. Line station.
How to tell you're in Snow Hill Tunnel (SHT)
The line north from Blackfriars station drops significantly to reach a 'new' underground station called City Thameslink (note: originally at this point, the line would have remained high to get to Holborn Viaduct Station). Almost immediately after this station you'd be in the SHT. Note the underground (cut and cover)-style of architecture now. Claustrophobic sidings etc. Look out of the right-hand window as the train peaks its speed for the journey and you'll the see the old signal box for Holborn Viaduct Station. After this note well where the train pulls in at Farringdon, close to the current met. railway. Soon after this, if you are very observant, you'll spot the original Kings Cross Met. station, some platforms running for quite a well (with garden plants still in plant boxes). Finally once you leave Kings Cross Thameslink look immediately to your left... (an old stair case!) Soon after Kings Cross Thameslink, you'll rejoin the original North London route again.
In the early 1990s, Holborn Viaduct station was demolished, along with its bridges.