Take them down,put warm water in your bath,lay blinds over side and gently clean with soapy water,sliding them in gradually,shower with clean water,put on line to dry.hoping this answer will help,as I do mine like this.
Thanks for all your responses. I followed Jackyp's advice (and the one that required less elbow grease!) and used the washing machine/pillowcase method. Glad to say they turned out fine. I only washed two slats a a time and they are as good as new.