Show on mapThis tunnel which is now a footpath to the NYMR engine sheds was originally built around 1834 by George Stephenson as part of the Whitby to Pickering Railway. Grosmont at the time was just known as “Tunnel”
 
The original carriages were horse drawn, but the the line was developed by George Hudsons’ York and North Midland Railway between 1845 and 1849, the large double track tunnel built just over a decade later shows the pace of development at that time.
If anyone is in the area the engine sheds are definitely worth a visit. The famous engine ‘Sir Nigel Gresley’ was there when I visited at Christmas.
A couple more views of the tunnel from the Southern portal
http://markt79.fotopic.net/p58122391.html
http://markt79.fotopic.net/p61376220.html
Sir Nigel ‘lives’there.
Opposite the old Ironworks on the other side of the tracks is an old brickworks, all the kilns are still there but on private land now.
If you go back through the trees at the end of the ‘top’ carpark where you took the pictures you will find an old tramway cutting that leads to the remnants of a bridge that crosses the Esk back to one of the ironstone mines, all the deck timbers are still intact.
In addition if you walk through to the hamlet of Esk Valley considerable earthworks and remnants can be seen relating to mining activity. I think Chris posted some details of this area a while back.
I have always been under the impression that the worlds first passenger tunnel was the one on the Whitstable toCanterbury Line ( known as the Crab and Winkle Line-see web site crab and winkle railway} which was opened in 1826 by George Stevenson some years earlier than the Grosmont Tunnel. but it would depend upon what criteria is used.
Perhaps thats why they’ve hedged their bets with a “?” at the end.
The website of the Crab and Winkle says Monday 3rd May 1830