Idk if this is on the Amazon UK site, but if you have a bathcaddy(great for reading!) you could Velcro-tape one of these warm closet lights to it. Not waterproof, but not necessary on a bathcaddy.
ZEEFO 6 Pack Motion Sensor Light, Battery Powered Motion-Sensing LED Night Light, Wall Light for Hallway, Closet, Kitchen, Step, Stairs, Bedroom, Bathroom, Nursery (Warm White) https://www.amazon.com/dp/B01MDKI6U4/ref=cm_sw_r_cp_api_I2qPybTTSZ7PB