The report leaves open questions to me.
The commander acknowledged this instruction and called
“GOING AROUND, REQUEST A HOLDING PATTERN
OVERHEAD CHILTERN OR OCKAM TO RESOLVE A
LITTLE FAILURE” but ATC were not advised of the
specific nature of the failure."
ATC did not reply to this request nor was the request passed on to the next sector. The specific nature of the failure is certainly not a requirement to issue a clearance as requested.
In the absence of any reply from ATC the crew carried out the standard missed approach procedure.
Despite a later decision to expedite the approach and accept a long low speed vector with high R/T load the original intention of the crew was to resolve a problem in a holding pattern with reduced distraction.