Barring any further solid information, I'd say this is exhausted SASless. SiloeSid's graphic tells the story clearly - it's just devoid of the actual weather over the Thames that morning.
G-CRST's failure to hold between Westminster &
VB - and not going east as far as London Bridge as offered - would seem to indicate that he was having immense vis problems.
(I'm not certain what the controller was seeing on the screen at 0758 when the tx was "you can make it quite a wide hold etc." G-CRST was already west of VB and into Class A. Did the controller see this? The radio message doesn't really match the circs.)
We also need to know who G-CRST monitored or spoke to on the northern Elstree-bound route. If you're going to overhead Batt at 0740, wouldn't you put in a call as a safety? It's not in the AAIB log.
And Elstree - doesn't open until 0900. So no tower, no weather - except for client telling him that his enroute to Elstree was bad. Could have diverted to Denham (0800 open) - but maybe couldn't see a route clear?
Let the AAIB finish their work.