It would be better if you'd just look up rule H3 of the highway code rather than keep saying the same thing, none of those references mean anything as they were nothing to do with filtering, one was car vs car, and because they are before the 2022 rule change 'heirarchy of road users'.. which is what is the important thing in OPs incident, there's even a picture to illustrate that a bicycle filtering from behind you has priority going straight on, and you have to give way to them before you make your turn, I'll include it but the tagline says "Rule H3: Wait for the cyclist to pass the junction before turning"
Bicycles are allowed to filter:
RULE 163: Cyclists may pass slower moving or stationary traffic on their right or left and should proceed with caution as the driver may not be able to see you.
Cars SHOULD give filtering cyclists priority
RULE 76 (for cyclists) - Going straight ahead. If you are going straight ahead at a junction, you have priority over traffic waiting to turn into or out of the side road
RULE 160: be aware of other road users, especially cycles and motorcycles who may be filtering through the traffic. These are more difficult to see than larger vehicles and their riders are particularly vulnerable. Give them plenty of room, especially if you are driving a long vehicle or towing a trailer. You should give way to cyclists when you are changing direction or lane – do not cut across them.
Heirarchy of road users (2022) determines that cyclists and motorcyclists are more vulnerable that cars and should be given priority:
Rule H3 - Rule for drivers and motorcyclists
You should not cut across cyclists, horse riders or horse drawn vehicles going ahead when you are turning into or out of a junction or changing direction or lane, just as you would not turn across the path of another motor vehicle. This applies whether they are using a cycle lane, a cycle track, or riding ahead on the road and you should give way to them.
You should not turn if a cyclist is filtering up behind you
Rule 211 - It is often difficult to see motorcyclists and cyclists, especially when they are waiting alongside you, coming up from behind, coming out of or moving off from junctions, at roundabouts, overtaking you or filtering through traffic. Always look out for them before you emerge from a junction; they could be approaching faster than you think.
Do not turn at a junction if to do so would cause the cyclist going straight ahead to stop or swerve, just as you would do with a motor vehicle.
Rule 180 (turning right into a side road) Wait until there is a safe gap between you and any oncoming vehicle. Watch out for cyclists, motorcyclists, pedestrians and other road users. Check your mirrors and blind spot again to make sure you are not being overtaken, then make the turn
I do think the rule is troublesome, as overtaking a vehicle about to turn is dangerous, and I can't think why any cyclist would do that deliberately as they are advised to use caution and not overtake at junctions, but the whole point of it is that filtering is perfectly legal yet a filtering cyclist may not be able to see you indicating, especially if your road position is poor, or if you are indicating at all.. so they need to put the onus on the car driver to give priority to the more vulnerable road user.. it isn't a MUST rule, but it is a should rule, and if you hit a filtering cyclist, that you should have given way to, because you didn't check for them then you will be in big trouble.. there are plenty of posts on here saying the same thing has been tested in court and the car driver is found 100% at fault if it is after 2022.
OP has had a lucky escape tbh.