I'm looking for preferably a raster which can be edited and reclassified which show population density in the UK. Alternatively, there is a data set available on ArcGIS online but some areas are NoData and I can't reclassify it. Is there a way to make it 'editable?'
Why don't you
All assuming you are using a nice projected boundary file so that your area units make sense.
the government would probably distribute geometry files (maybe shapefiles) which would contain the geometry data ... and have attribute files containing the attributes you need. you join them together, and do the calculations if required in the attribute table. If they had population density available, then your task would be one step closer to being complete. Often, you need to take what is available and piece it together to get what you want. All information is available in the help files and on basic tutorials within esri depending on your comfort level in using ArcMap