Yes, they do!

They accept that and everything else listed by WRAP Recycling Action Program (WRAP) on their website.
WRAP is a national public awareness and outreach initiative designed to make plastic film – including wraps, bags, and flexible packaging – a commonly recycled material with a strong and ever-growing recycling rate.
So, don't throw it away! Reuse or recycle your bubble wrap to help divert more from our landfills.