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I've spoke to drivers who do this before and a number of them will say they feel you should stop/giveway to everything as you are cycling and they should never need to slow down ever as they are driving. I wouldn't stress about it, moving over a bit or slowing for a couple of seconds to let someone out is reasonable and what they would most likely do for other drivers.
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I had this just a few days ago when I was fully loaded on a tour.
I put my arm, signalled, looked over my shoulder and saw the car. There was tons of room but as I started moving out to go round the bus I noticed the car behind had not slowed at all and was just bowling down the road. I stopped my move an put my arm down but the driver still leaned on their horn as they came past me. Presumably infuriated I had even contemplated moving out.
They don't have to let you out but I'm sure they would bang on their horn if this was done to them.
Shit drivists are shit.
Travelling at speed down seven sisters road and a bus is pulling in ahead of me, so I start pulling out. Driver in the next lane (who is well behind me when I start to move over) fails to slow or even move over slightly to give me space but instead leans on their horn and blasts past me as I'm alongside the bus. Slightly lost my shit and did some ineffectual yelling when I caught up with them at the lights, which I'm not proud of. And then started doubting whether I was in the right. Off to check the bad cyclists thread!!
I hate that road. :(