It's because the data behind the network analysis service that this sample uses (http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Network/USA/NAServer/Service Area) only covers the US and Canada. This service does not have the road network data for the UK.You can either use the ArcGIS World Network Analysis Service, which covers 145 countries including the UK, OR set up your own network analysis service with UK road data.If you already have an ArcGIS.com subscription, just replace the URL in line 49 in the service area demo with the URL to the service area task on the world network analysis server:serviceAreaTask = new esri.tasks.ServiceAreaTask("https://route.arcgis.com/arcgis/rest/services/World/ServiceAreas/NAServer/ServiceArea_World");
It would prompt a log-in box to ask for your ArcGIS.com account credentials when executing the service area task.