Read this?
"What I saw this morning was not good: a helicopter flying at about 500ft eastbound along the Thames helicopter route. As it was just passing over Chelsea Bridge" from
Visibility must have been zero, or close to it... The helicopter flew straight into dense fog. As a former pilot, this struck me as peculiar, to put it mildly' - Comment - Voices - The Independent
Actually the times do not tally. The witness has a precise time of 7:37 logging into his gym. The flight left Redhill at 7:35. The BBC quote the crash at around 08:00.
The crash site is more consistent with the aircraft heading south, possibly following the river, and possibly missing the sharp bend to the West due to loss of loss of visibility. (Last points pure conjecture obviously)