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Dear Friend,
Not yet, there is no direct rail link. However, this is part of the plan to connect the two countries through, land, aire, sea and space, cyberspace (fiberglass network).
Rail links are planned. Pak railways need to upgrade first as well. For now the planned route is through GB just like the road. In a decade or so you can take a train in any major city of Pak and you will end up in China.
The simple plan is full integeration of Pak economy into Chinese and EEU economic spheres.
When the train connections are laid...you would be able to ship directly to EU all the way to Britian and of course, vice versa.
So very best of luck...however, a lot of work needs to be done by your Gov and peoples as well.