About 10 days ago I positioned from Barcelona (amber list) to London to revalidate my LPC in the sim (not under airline duty). The layover was about 24 hours.
Whilst the guidelines clearly indicate you are exempt from travel testing requirements and quarantine, I paid for the antigen test (cheaper than PCR) as my 'pre-departure' COVID test as a back-up.
The sim centre created a letter justifying the reason for travelling.
Check-in staff at BCN required my crew ID, UK PLF (which stated that I was exempt) and letter from the sim (I highly doubt they read it fully).
Upon landing at LGW, officers (before immigration( verified my reason for travel and checked my crew ID.
Immigration officers did not ask for any proof other than a verbal declaration.
Let me know if you need more info.