Have you read BIMM's
Undergraduate Academic Assessment Regulations?.
Section 22, "Second Retrievals (Level 6 only)" starts by saying:
"22.1. If at Level 6, you have failed to meet the award requirements for your course as a result of failing a single module that does not qualify for Compensation (following any Retrieval offered), a Second Retrieval opportunity will be provided by the Assessment Board where there is evidence of engagement with the module in question."
So, the first item of interest is the phrase "a single module that does not qualify for Compensation". The fact that you have pointed-out that this module is a Core module suggests that you believe that this makes it
ineligible for Compensation. Is that the case? What has lead you to this conclusion (I don't see it mentioned in the Academic Regulations).
To the contrary, Section 19, "Compensation", says:
"19. Compensation
19.1. Compensation is applied at each Level of study for a Marginal Fail.
19.2. Compensation will automatically be granted for up to 30 credits, provided that you have passed the remaining 90 credits at each Level and achieved an overall mark of 40."
This would tend to suggest that, as long as your
overall mark is at least 40, that this 30 credit module should be subject to Compensation.
It might also be worth having a read of section 23, "What happens if I don't pass all my modules at level 5 or 6?"