Most Roller Blinds are Polyester.
Most Manufactures recommend laying them flat and cleaning with a mild detergent.
I have had customers who have put while vertical blinds in a bath with bleach and they were Ok But as a blind retailer I could not recommend this
There are some verticals that can be machine washed I went to a call once when a lady had been told by a salesperson that her blinds were washable so she put them in washing machine as her previous blinds had been machine washable .disaster she compounded this by ironing the blinds complete and utter disaster.
Extracta and Ashbys used to ave a hand tool for cleaning blinds so it must be possible to clean with HWE. using a mild cleaner.
I did try with an upholstery tool while blinds were hanging but limited results.
A good roller blind is about £100 plus although you get companies on ebay selling DIY Blind at post manufacture prices like in carpet cleaning devaluing the trade
www.ideal-blinds.co.uk