I have roller blinds on my windows. The ones that pull down and are spring loaded to return to the top when you give them a tweak (they fit with the 1880s style of the house). We call them Holland blinds but no idea what you call them in the UK. They are great for privacy at night, but during the day as they are raised, they do not give any privacy at all so when I find something suitable I will be hanging lace in the lower sash to block people from peering in the house when I am out and about. The cats are generally pretty good with these, though the ring on a string that pulls them up and down could be tempting for a playful cat. Smidgen will shove his head up under the bottom of the blind when he wants to look outside at night, but this does not seem to cause any damage.
You can get modern ones that are fixed to a track at the sides which allow light in, and a view out, but privacy when people look in the windows. The reverse, obviously happens at night so they need to be supplemented by curtains if you require privacy. They would be good with cats as they are fixed into their tracks at the sides and so can not be pushed or pulled around.