I am using Jquery UI Drag and Drop ( http://jqueryui.com/demos/draggable ) together with https://github.com/furf/jquery-ui-touch-punch to map touch events over to mouse events.
I solved this by switching from https://github.com/furf/jquery-ui-touch-punch to the code in this solution: Javascript Drag and drop for touch devices.
In the end all I needed to adjust was to remove the event.preventDefault();
to re-enable scolling.
Edit
Basically I used the code from the second answer I linked - with some adjustments. Here is the JS fiddle of my solution, hope it helps: http://jsfiddle.net/LQuyr/8/