Fiona, character isnt something that a house 'has', it is something that is put there by the ppl who live in it.

My darlink sister just bought a brand new ultra practical townhouse, which surprised all of us cos she was wanting "character" to the point that she was contemplating building her own ala mudbrick (!!) and...well, it HAS character because she has put it there. She started again with all her furniture etc and it looks fabulous. She is happier than a pig in (characterful) mud.