The discovery of the first authenticated biblical scripture in Anglo-Saxon from an ancient attic in a Manchester suburb could provide important clues
of determining, in addition to how, when continental Europeans colonized the British Isles.
A. of determining, in addition to how, when continental Europeans colonized the British Isles --- of determining is a wrong idiom in the context.
B. in the determination of how and when the British Isles were colonized by continental Europeans ---
-in the determination of is not concise. C. to determine how continental Europeans colonized the British Isles and when they did --
The second is just dangling without completion. In additions, 'they' is rather problematic. 'It' may stand of Europeans or even clues (The discovery of the first authenticated biblical scripture in Anglo-Saxon from an ancient attic in a Manchester suburb could provide important clues
to determine how continental Europeans colonized the British Isles and when the clues did (provide) D. for determining when the British Isles were colonized by continental Europeans and how they were ---
for determining is the correct idiom. However, the second part has the same problems as in C. E. for determining how and when continental Europeans colonized the British Isles --
Best of the lot with the problems posed in C and D altogether avoided.