Not sure where you are in the UK but Carshalton Lavender have glass lip balm jars with a plastic screw lid. They are 15ml in size, slightly larger but very nice.
People could bring these back for refills (throw away the lid and sterilize the glass jar) or recycle them in the seperate bins.
Could you use the tins and make a refill for the tin, I do this with my solid lotions. My testers really like the idea of the refill, less garbage for the landfill and less expensive for the customer. I shrink wrap the refills.