No. Your UK institution is not an eligible institution which explains why there is no form 1098-E.
The student loan interest deduction is interest paid on loans used for qualified education expenses. Qualified education expenses are items paid to attend an eligible institution. According IRS Publication 970 (here) page 32 an eligible institution is:
"...generally any accredited public, nonprofit, or proprietary (privately owned profit-making) college, university, vocational school, or other postsecondary educational institution. Also, the institution must be eligible to participate in a student aid program administered by the U.S. Department of Education. Virtually all accredited postsecondary institutions meet this definition. An eligible educational institution also includes certain educational institutions located outside the United States that are eligible to participate in the U.S. Department of Education's Federal Student Aid (FSA) programs.
The eligible institution will issue a form 1098-E on interest paid.
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