Special toilet paper?

No not the question you think I am going to ask 

Our van has a slot in the cupboard under the sink where you can put a toilet roll.   My problem is if you put a full British bog roll in it snags and breaks until the diameter of the roll reduces as the paper has been consumed.  On our Holliday in Spain
and France we realised that continental bog roll works perfectly from a dispensing point of view.  After careful investigation we realised that the core on a SBBR (standard British bog roll) is a greater diameter that its continental counter part.  Presumably
because it makes the roll look thicker and therefore got more sheets, when in reality they are selling air. This seems to apply across the brands.

So my question does anyone know of a source of toilet rolls that have a slimline core.  Or are we going to have to start them off at home and then take part used rolls away in the van?  A bit like part worn tyres I suppose.