It sounds like your problem is to do with the OS raster product drawing at the wrong scale. You'll find information about recommended scales on the OS website. Effectively showing the 250k mapping product at a whole UK level would cause QGIS to simplify the data and you will lose some of the detail of the map, including the grid squares. You might want to think about the scale of the mapping you are using.
There are a couple of things you could do.
1) In the composition section of the Print Composer you'll see there is a resolution option under "Paper and quality" - you can increase this a bit and that may help a little when you export the data to a graphic or pdf.
2) You could manually put in the grid lines using the "Show Grid" options in the item properties of the map.
3) You could try to do something with the pyramid options which you will get if you right click on the raster layer and click on the "Pyramids" option - try a different resampling method and see if that helps.
4) Download the OS Vector datasets for the mapping you want to use and use these to display the data.