As I see it they both committed three violations of the law as set out in the Traffic Sign Regulations and General Directions 2016 -
Car driver violates:
"a vehicle entering the junction must give priority to vehicles coming from the right at the transverse road marking"
Cyclist violates:
"vehicular traffic approaching [such] a junction should give way at, or immediately beyond, the line to traffic circulating on the carriageway of the roundabout"
Both violate:
"a vehicle proceeding through the junction must keep to the left of the white circle"
"no vehicle is to proceed past the [white circle] in a manner, or at a time, likely to endanger any person, or to cause the driver of another vehicle to change its speed or course in order to avoid an accident."
I think the words of the cyclist at the end are important: "I now don't trust any drivers so I'm much more twitchy around vehicles until the moment I'm sure they've stopped, seen me and are not pulling out." That's probably how most sensible novice cyclists approach things.
Who'd have thunk it was so hard for two people to use a junction? I assume therefore that when self-driving cars (and tricycles or whatever) become the norm, cyclists will have to be banned from most roads.