Indurain's Lungs
Legend of Garry Nelson
Although it's hard to see it looks like the Taxi did: No Mirror - Maneuver - Signal. If this is the case the taxi is 100% at fault, and anyone saying otherwise should probably not be on the road! The number of drivers that can't seem to draft Mirror-signal-maneuver is frightening, particularly indicating when halfway through a turn.
I don't think you can say no-one is to blame as that suggests it was unavoidable.
You know which side of the fence I'm usually on but I don't think you can blame the taxi 100%. The cyclist is on the inside at a junction, that's the number 1 killer of cyclists in London (usually HGVs though). I'd be slowed to a crawl in that situation anticipating a turn.
Yes, the taxi should have checked more fully and indicated earlier, but he's not 100% to blame.