Re: If he gets his way...
"You're right that the Convention isn't UK law (few treaties explicitly are), but invoking that loophole puts you on exactly the same thin to non-existent ice as detaining a courier - it's a flagrant breach of international law."
Not in this case because the UK is not explicitly signatory to the Vienna Convention. The Diplomatic Privileges Act is not the Vienna Convention and has various local alterations as noted. The local override is one of them. Plus there's also the matter of abusing immunity (talking the mick, as another put it). You mention the Yvonne Fletcher incident but neglect to mention they couldn't pin the culpability to a single individual due to (1) there being more than one shooter and (2) secrecy concerns. Plus it should be noted the UK got theirs back. They severed diplomatic relations with Libya and allowed the US to bomb Libya from bases in the UK in retaliation. Plus Libya eventually paid compensation for the incident, probably because they had no friends on northern Africa.
This time, we know exactly who the culprit is, he hasn't made any move to conceal his crimes, so as the saying goes it's open-and-shut. Any attempt to use diplomatic immunity to try to get him out can and would get called out as abuse of immunity. About the only reason the UK doesn't sever diplomatic relations with Ecuador is that Ecuador DOES have friends in South America which can result in reprisals. And while there is little the UK needs that comes from Ecuador, other South American countries may have products of value (like say Venezuela with its petroleum).
"That's an awkward position to be in since you're explicitly asserting that local statutes trump the Convention which means that you're agreeing that Afghan blasphemy law (for example) overrides the immunities of our people in Kabul."
That depends on the laws specifically set down in Afghanistan. If blasphemy laws explicitly take precedence over anything the Vienna Convention defines, then you're up the proverbial creek. I strongly suspect this was very much the case when the Taliban had full authority there, thus the lack of diplomatic relations there at the time.