Here’s a better close-up photo of it, from MS Live Search. Much better and clearer than Google Maps, in my opinion. Plus, you can see the same spot from any of 4 directions.
I think that in Britain, roundabouts that are so busy that such lane-crossing problems arise tend to be regulated by traffic lights, at least in peak hours, essentially reverting to something resembling America-style intersections. Roundabouts work best with light to medium traffic. Judging by the number of lanes entering the OP’s traffic circle and the number of cars visible in the photos, I think that that roundabout would be a candidate for traffic lights around it.
Now that I see it, I’m not sure about the OP. Seems like a rather simple traffic circle. It looks like they’ve even painted lines to make it simple to negotiate, and it vaguely represents a modern roundabout.
The most important thing on large traffic circles is to make sure you get into the correct lane before you enter it.
This one looks fairly striaghtforward, you join at some point, and if you are in the right lane on entering the circle, you stay there but you must take the next exit off - that is shown by the paint markings.
If you wish to go further around than the next turn off, then you join the circle in the left lane, and go around, and move over to the outside lane only when you have passed the exit previous to the one you wish to leave by.
You must use your indicators to show you are changing lanes.
There should be no one on the outside of you as you switch to the outside lane, because traffic should either be waiting at the previous entry for you to pass, or any traffic thaat is outside you, should leave the circle at the exit previous to the one you wish to leave by.
This is assuming everyone understands the system.
You should try out some of the horrors over here in the UK, there is no way you can drive aggressively, and you really do need to plan your route around, we have three lane circles, and then there are one or two legendary ones which have circles on each of the entry roads too.
Take a look at this - Armley Gyratory
http://www.pbase.com/clivegriffin/image/41721468
At the lower right edge you can make it out, this has umpteen lanes coming and going on it, and is notorious.
I’m with Balthisar and casdave, that those images make it clear that being in the correct lane to start with is all that is necessary.
I don’t see the fuss about Amrley - it just looks like a large inadequate motorway junction (e.g. South Mimms). What you needed was the
Hanger Lane Gyratory, obviously!
Plus, Swindon doesn’t have the monopoly on magic roundabouts: Colchester has a pretty good one, too.
Twenty four posts until the Swindon Magic Roundabout link. That could be a record.
And no, those big gyratories are not representative of the roundabout form. The first time you encounter Hanger Lane, it’s intimidating even if roundabouts are in your blood.
It’s the opposite of Mornington Crescent threads, isn’t it? 
I haven’t seen a link to this video of driving through it before, though. (Warning: bizarre choice of soundtrack!)
Hell, yeah!
Ah, the gritty urban sound of Swindon. But that magic roundabout thing does work. As I think I’ve said before here, while driving though it you merely experience it as a succession of innocuous mini-roundabouts. At no point do you perceive that you are passing through the road traffic equivalent of a four-dimensional hypercube.
Long Beach, CA. First advice: traffic circles are not for the faint of heart. If you have any doubts, find a way around. Longer, but cheaper than follow-up therapy. Next, as said above, traffic on the circle has right-of-way. Slow down, even stop if you must, to wait for an opening. (This from a Californian, so you know it’s not said lightly.) Thirdly - this is a dream, not an experience - use your turn signals.
If you can get through the traumatic experience in one piece, you’ve done as well as can be hoped: good job.
I wanted to correct some misinformation here about navigating roundabouts. I’m from New England, the home of the “rotary,” which is basically just the New England word for roundabout. Yes, there are technical differences, but the general rules are the same.
#1. Yield to left. Traffic entering should yield to ALL lanes in the rotary, and should never pull in alongside a car in the inside lane. Traffic in the outside lane of the rotary should yield to traffic on the inside lane signalling to exit.
#2. The outside lane is for going halfway around or less (straight ahead or right, if the island weren’t there). Anything beyond that (going left) and you should use the inside lane(s). The inside lane(s) may be allowed to exit along-side the outside lane at the 12 o’clock exit, if the lane configurations will allow for it. It creates no conflicts if everyone chose their lane correctly ahead of time.
A picture is worth a thousand words, so check out this graphic that shows how you should use the lanes as a general rule.
http://www.dmv.ny.gov/olderDriver/images/multi-lane.png
Those are the general rules – the rules you follow if there are no signs or markings dictating otherwise. Obviously signs and markings take priority over the general rule.
A note on lane usage: you shouldn’t do any lane changes on entering the circle. If you need the inside lane, turn directly into it, don’t turn into the right-hand lane and then make a potentially unsafe lane change to the left.
Signalling is also a good idea. You should put on your right blinker as you pass the exit prior to the one you want. For example: If you’re taking the second exit, put your blinker on as you pass the first. If you’re taking the first exit, put your blinker on as you approach the rotary. If you need to change lanes to exit, use the same procedure as you would for any lane change.
All of these rules, but the number one unwritten rule of the rotary is this, don’t expect any other drivers to follow them. They’re not covered all that well in drivers ed courses, and many people just point their nose where they want to go and gun it, paying no attention to yield signs or lane-usage rules.
The traffic circle linked to by the OP is not confusing.
Check out this monstrosity near where I live. If you include the western approach road, it actually spans three counties (I’m not making this up).
When I was taking driving lessons nearly 20 years ago, it didn’t have the small dotted lane markings. I’m not sure whether they make things easier or harder…
I was so sure that was going to link to the Swindon “Magic Roundabout.”
Ha! That would be too obvious. The Magic Roundabout isn’t even that complicated.
Is there a wayback machine for google, so we could see what the OPs traffic circle looked like five years ago when the post was made?
I had a feeling that was going to be the response. 
I’m sure it’s not complicated and perfectly logical after you get a few passes through it, but it sure looks like a total mindbender. For those that don’t know, it’s a giant roundabout with five roundabouts nested within it. The inner roundabouts go clockwise, while the outer roundabout (in which they are all nested) goes counter-clockwise. It actually does make sense when you look at it and think about it, but it looks completely insane.
It’s always described that way but in fact the outer roundabout in as much as it exists at all can be driven in both directions - I don’t really understand what people are getting at.
I was giving a cab driver in DC directions to my house and said “stay on New Hampshire as you drive through the circle,” and he literally tried to drive straight through the cirlce and almost drove up on the sidewalk.
I asked him what the hel he was doing and he said “you said drive through the circle!”
I don’t have an answer for the OP, I just like that story.
No it can’t. Look at the lane diagram. You can either go round the outer roundabout clockwise, by taking the first exit off the mini-roundabout you join at, or you can go round the inner roundabout anticlockwise, by taking the second exit.
You can just think of it as 5 separate roundabouts connected by ordinary two-lane roads. Like the one in High Wycombe, but more compact.
“Look kids! Big Ben! Parliament!”
But this is susceptible to the rather huge problem that it requires everybody to know, before entering the circle, how far around the circle their intended path departs.
What if a conceptually “straight” path–continuing on the same-named artery–actually constitutes a net left-veer?
So–what’s the point?