The Danish tv-channel DR1 has been visiting the Danish rail network for a few months, and on their website, you can now take the front seat on various routes such as the beautiful private railways of Northern Sealand, the long mainline from Copenhagen to Frederikshavn (5 hours long) and the international line from Helsingør to Helsingborg (Sweden)
http://www.dr.dk/HD/paa-skinner/index.htm#/26120
Our scenery is not nearly as beautiful as the one you have in Britain, but I hope you guys will enjoy your little "visit" in my country