Good question. Here's why.
Plastic bags in food waste
When you use plastic bags in your food waste caddy you're simply using them to contain the food, and keep your caddy clean. They don't get recycled.
In fact, the first thing that happens when your food waste gets to the recycling plant is the plastic bags are all dredged out. They're sent off for burning along with normal refuse to generate electricity. After that, the food waste can be recycled.
We used to ask you to use bio-liners to line your food waste caddy. But the food waste recycling companies found that the bio-liners composted much more slowly than the food. That slowed the recycling process down, and made it much more expensive. They tried dredging the bio-liners out of the food waste, but th sticky bio-liners got tangled around the dredging equipment. Cleaning them off was very expensive.
The recycling companies found that using plastic bags was, overall, much more cost-effective. They're not recycled but good stuff still happens to them. And you can use old bags like bread-bags or carrier bags if you like.
Plastic bags in recycling bins
It's always been expensive to recycle plastic bags. And it's costly to separate them from mixed recycling, too.
In 2018, it became even more expensive to get plastic bags recycled, after China stopped accepting huge quantities of recycling that it had previously imported from Europe and elsewhere.
Epsom & Ewell's recycling stopped going to China many months before the ban, thanks to some forward-thinking by the company that deals with our dry recycling. But it has still become uneconomical to get some plastics recycled - like bags, film and some hard plastics. In a commercial world, recycling companies simply don't want materials that won't make a reasonable profit.
Good stuff still happens to them, of course, because the contents of your black refuse bin are burned to generate electricity. It would be better if we could get them recycled, but it doesn't look like there are any opportunities to do that at the moment.