There are multiple opportunities for internships (both paid and unpaid) for library students. The following list will give you a starting point for finding internships, but it is by no means exhaustive.
LIS Listserv
- If you're not already subscribed, the above link will give you details on how to subscribe to the LIS listserv under the "Current Students" heading. Jobs, internships, and other announcements are frequently sent out making it a great resource.
Internship Resources through the Career Center
- As a UK student, you have access to the resources and services offered by the Stuckert Career Center. The above link will take you to a page that lists various websites/organizations you can check with to find internships.
Idealist.org
- This site allows you to specifically filter for internships to find what's available and what you're interested in.