It seems that in 1998, presumably in response to 1996’s National Cycling Strategy, the DfT were trying out “innovative schemes” as they do every decade or so in order to put off doing things that have actually been shown to work. The council volunteered Weymouth’s Westham Roundabout, a busy junction between the Town Centre Relief Road and the main road to Portland, for a cycle lane to be painted around the edge. On the carriageway, of course, not done properly like the Dutch would do. Today the Rodwell Rail Trail ends at this junction, but the opportunity to do something truly great for cycling here was passed up again when the roundabout was converted to a complex high-capacity signal-controlled cross ahead of the 2012 Olympics.
Note the Echo’s particularly absurd transport mode tribalism fail: “positive discrimination”.
Highways and byways in Dorset 
That’s an interesting one to see. Sounds as if it were a far closer attempt at a “Dutch” roundabout than what happened more recently in Bedford.
Also “Dog’s teeth” (they’re from sharks in NL) were used as give-way markings on this roundabout. I’m sure I’ve been told that’s impossible more than once.
There are roundabouts in NL where cyclists are expected to go around the edge on carriageway. I showed you one in Groningen – one of several bad examples from that city. It’s not very good. Actually, it’s dangerous and should be replaced. The design of roundabout used in Assen is safer than that used in Groningen. It’s also far more likely to work with British drivers.