I wonder if a return for cash scheme could work in this case, as it does with cans and plastic bottles. This way people could get their 5p/25p back and there would be a near universal collection of the cups for recycling. Or there could be a great new venture for an entrepreneur, looking to make energy from the cups. Similar to what Sweden is doing on a national scale: https://www.blueoceanstrategy.com/blog/trash-treasure-sweden-recycling-revolution/