England fought to retain control over the Falkland Islands because of the islands’ geographic convenience; the British feared that if they lost the Falklands as a stepping stone to the South Atlantic, their trade with more distant colonies was always jeopardized.

A if they lost the Falklands as a stepping stone to the South Atlantic, their trade with more distant colonies was always jeopardized
was always jeopardized is wrong
B without the Falklands as a stepping stone to the South Atlantic their trade with more distant colonies would always be in jeopardy
Correct
C their trade with more distant colonies was always in jeopardy if they did not hold them
them does not have a clear antecedent
D losing them as a stepping stone to the South Atlantic would jeopardize British trade with more distant colonies
them does not have a clear antecedent
E always would their trade with more distant colonies be jeopardized if they did not hold them
always would is not proper
_________________

The intended meaning is the British fear that their trade will be in jeopardy. But the action happened in the past ==> We need to convert "will" to "would".

Only B and D are contenders. However, "loosing them" in D is incorrect. Cause the Island is singular.

Hence, B is correct.