The film you want is NARA publication T843 from Record Group 85.
The passenger list is on FamilySearch.org. (You may need a free account to see it.)
The direct link to the first image is https://www.familysearch.org/ark:/61903/3:1:33SQ-GY7R-PL1?i=56&wc=M6B4-4M9%3A219561801&cc=1923995
Brittania starts on page 28 (small, handwritten or typed in a top corner), but page 28 is on image 57 of 659. The Brittania lists go through to image 90. One page of a passenger list is split into two, so if you find the name you want, make sure to look at the next page.
If you need to find it the long way:
--Go to www.familysearch.org
--At the top of the page, hover over the word Search & then click Catalog
--Click on "Title" & in the Title box, type or lift Massachusetts, Boston Passenger Lists, 1891-1943
--Click on result
--There will be a line in red that says "Massachusetts, Boston Passenger Lists, 1891-1943 are available online, click here." Click on the word "here."
--Click on the red sentence near the bottom of the page that says "Browse through 335,814 images."
--Scroll & click on "269 - v. 439-440 Oct 1, 1921 - Dec 31, 1921" (middle column)
--Go to image 57 (change the image number above the left-hand side of the image)
I hope this helps. Good luck!
Dear Ms. Eastman,
Thank you for posting your request on History Hub!
We suggest that you “browse” the Massachusetts, Passenger and Crew Lists, 1820-1963 collection by date on Ancestry. The Boston port records are arranged by year and month. You will have to search for the correct vessel within the images. For the October 1921 set, the 10/12/1921 Britannia entry begins at Image 284. There may be a fee for using Ancestry to access digitized records. However, you may view these records online at one of NARA's facilities for free via a NARA PC. For the nearest NARA location, please consult our web page at https://www.archives.gov/locations/.
We hope this is helpful. Best of luck with your research!
[Information provided by Elizabeth Burnes, Subject Matter Expert]