Thank you for posting the link to the AAIB report and indulging me on the question of whether alternate airports should be sought. Doing a bit of reading I came across the following to confirm what has been mentioned here. Glad to hear that manuals have been amended to no longer include the following.
From the G-VSKY AAIB report (1.18.3):
There is an agreement with Heathrow ATC and LATCC that the ODM may request the following message to be passed to an inbound aircraft with a technical problem that has potential to block a runway:
'This is a message for the captain of (aircraft callsign) from Heathrow Airport Limited. Your technical problem could cause a runway to be blocked at Heathrow; you are asked to consider an alternative, less busy, airfield rather than risk major inconvenience to other operators.' This message is not intended to be passed if the aircraft has declared an Emergency (Mayday or PAN), has a fuel shortage, or when a diversion would increase any risk to the aircraft
Especially the part about 'risk[ing] major inconvenience to other operators' would have hit a very sour note with beardy I presume.