Can I just wear normal trainers or do I really need specific badminton shoes? They seem expensive for something I might only do once a week.

Please do not play in running shoes! This is a safety issue. Running shoes have grip patterns designed for forward motion. Badminton involves lots of lateral movement and sudden stops. Running shoes will grip the floor wrong and you WILL roll your ankle eventually. You need non-marking indoor court shoes at minimum. Budget options like the Asics Gel-Rocket (around 30 quid) are perfectly fine for beginners.

Coach Sarah is right. I played in running shoes for my first month and twisted my ankle badly. Proper court shoes were the best investment I made. They do not have to be expensive - even a 25 quid pair of indoor court shoes from Decathlon is infinitely better than trainers.

Also your sports hall may not even let you play in non-marking shoes. Most will turn you away at the door if your shoes leave marks on the floor.