@Niamh05 If you're an OS customer I'd suggest using OS Build and Select Recipes to extract the carriageway/highway data. From your image above you're missing the footway/footpath data so, unless you don't actually need it, you're seeing what's to be expected. For a start, the Carriageway/Highway data is under Transport/Road in the recipe builder.
You won't find carriageway/highway data as polygons under Open Data and, across the UK, not every local authority has a completed road polygon dataset, so OS really is your first and only option of a complete dataset.