Thank you for the question. First I'd like to say that depending on where you decide to attend school, you may not have to double major at all. Some colleges offer "English Literature and Theatre" as a single major (note that English and British are often used interchangeably within the context of literature).
I should mention that many schools are located in the UK which may not be feasible or desirable for you, but I'll provide the links just in case. In the U.S., Reed College in Portland, Oregon offers a single major called "Literature-Theatre: https://www.reed.edu/catalog/programs/interdis_majors/litthea.html
For schools in the UK you can check out:
University of Reading: https://www.reading.ac.uk/ready-to-study/study/subject-area/english-literature-ug/ba-english-literature-and-theatre.aspx
University of Leeds: http://courses.leeds.ac.uk/24221/BA_English_Literature_and_Theatre_Studies
University of Warwick: http://www2.warwick.ac.uk/fac/arts/english/applying/undergraduate/courses/qw34/
These programs and colleges are limited to English Literature and Theatre as a single major. I am not suggesting that these are the only possibilities. You can also consider:
Also, depending on which school(s) you are interested you may have to pick a closely related field for a double major or doing a major/minor. For example, you may end up majoring in Theatre and minoring in English or vice versa.
Sometimes double majoring can lead to double the work if the fields aren't closely related. You can read up on this at these links:
Both of these fields are part of the liberal arts so may not have to pull "double duty" as much as if you electing to major in both Theatre and something completely unrelated such as Business Administration. Minoring is also a good option, but keep in mind that you will take few courses related to the field than if you were majoring in it. The plus side is that it will likely cost you less in terms of tuition. Double majoring requires more credits which can increase your tuition costs and the time it takes to earn your degree.
I know this is a lot to absorb, but I hope it helps you get started. Best of luck!