Despite of the political signal for a closer UK-US relationship, UK's

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Here is a detailed explanation to this question-

Meaning is crucial to solving this problem:
Understanding the intended meaning is key to solving this question; the intended meaning of this sentence is that despite there being a particular political signal for a closer UK-US relationship, UK's defense procurement here at times runs into problems and export licenses are delayed because of the inter ministerial differences.

Concepts tested here: Meaning + Idioms

• “although” and “despite” are used to show contrast.

A: This answer choice incorrectly uses the unidiomatic construction "Despite of"; please remember, "despite" is a correct idiomstic construction used for conveying contrast.

B: Correct. This answer choice uses the phrase "Despite the political signal", conveying the intended meaning - that despite there being a particular political signal for a closer UK-US relationship, UK's defense procurement here at times runs into problems and export licenses are delayed because of the inter ministerial differences. Further, Option B correctly uses the idiomatic construction "despite". Additionally, Option B is free of any awkwardness or redundancy.

C: This answer choice alters the meaning of the sentence through the phrase "In spite the political, signaling"; the construction of this phrase leads to an incoherent meaning; the intended meaning is that despite there being a particular political signal for a closer UK-US relationship, UK's defense procurement here at times runs into problems and export licenses are delayed because of the inter ministerial differences.

D: Trap. This answer choice alters the meaning of the sentence through the phrase "Despite the political signals"; the use of "signals" incorrectly implies that despite an indeterminate number of signals for a closer UK-US relationship, UK's defense procurement here at times runs into problems and export licenses are delayed because of the inter ministerial differences; the intended meaning is that despite there being one particular political signal for a closer UK-US relationship, UK's defense procurement here at times runs into problems and export licenses are delayed because of the inter ministerial differences.

E: This answer choice uses the needlessly wordy phrase "In spite of the fact of the", leading to awkwardness and redundancy.

Hence, B is the best answer choice.