Beetroot leaves being eaten

[lily]

Does anyone know what could be eating my beetroot leaves? Not flea beetles as they aren't getting holey, but being eaten from the tops downward. I asked at a nearby garden centre in the advice section but despite referring to a large handbook the man was at a loss. Does anyone know if mice/rats would do this?

[Oola]

Could it be weevils? I think they pretty much like to munch on any tender leaves don't they? Also, wouldn't be surprised if it was mice either. Sorry can't really offer up any other ideas.