waynedl:
I did point out in my OP that the lane markings put doubts in my head, I was always taught that the white lines were like ‘give way’ and if you wanted to cross them, then you had to ‘give way’ to anything the other side of those white lines.
The white lines are lane separation lines, because they’re broken white lines like on any other road you can cross them when safe to do so, in this case it wasn’t safe to cross the white line and change lanes because you had no way of knowing where the car on your left was going.
waynedl:
But, this road is clearly 2 lanes to go straight on, and nowhere on approach to the roundabout does it say “use both lanes for a right turn” or anything similar.
That’s where you’re making a mistake, there are only two lanes and they both go right round the roundabout as far as Park Way, there’s no need for a sign because the lane markings speak for themselves.
If either of the lanes were specifically for vehicles to turn off the roundabout the lanes themselves would turn off the roundabout, the way the nearside lane does for the Park Way exit, in fact that’s the only exit on that roundabout where you could reasonably assume that the vehicle in the nearside lane was turning off the roundabout.
waynedl:
In fact, with the road markings the way they are, you actually CAN’T turn right onto Westinghouse Road from the right lane unless you went all the way around the roundabout which would be madness.
I’m not sure what you mean, but getting onto the roundabout at Park Way I would take the outside approach lane then get into the lane nearest the island and move to the nearside lane around the Village Way areas so I could turn off into Westinghouse Road, there shouldn’t be a problem.
waynedl:
The only place the lines actually do what they’re supposed to do, and that’s corkscrew off, is back onto Park Way towards the M60 J9, other than that, they just do a complete circle.
Surely then, we only need 1 lane on all approach roads for that roundabout?
Why would you say we only need 1 lane approach roads 
There are two lanes on the roundabout and they can both be used safely if proper lane discipline is used, by proper lane discipline I mean you get into the most appropriate lane safely and in good time, and change lanes safely and in good time to get into the most appropriate lane for your exit from the roundabout, often that’s easier said than done on roundabouts but that’s just the way it is, in most cases unless the white lines show differently the most appropriate lane for exiting a roundabout is the nearside lane.
In your case, assuming the car had come from Park Way, the car driver was not in the most appropriate lane, but nor was you I’m afraid, the only real difference is that you moved into his lane when it wasn’t safe to do so.