Granted, they can be faster than two way roads.
I'm not sure I buy the idea that being overtaken by flowing traffic is more dangerous than navigating congestion though - where you have to pass through narrow gaps, potentially through blind spots, risk being crossed by lane changing traffic, risk being left in a dangerous position if the traffic lights change and so on...
Austen: "It's a great way to encourage pavement cycling too, it seems."
That's like saying traffic lights encourage red light jumping, so we souldn't have traffic lights.
London cycling campaign: "They have no other benefit than speeding up through traffic "
You put it like that but someone in favour of them might phrase it "reducing congestion" - which is of course good for pedestrians, cyclists and motorists. (It's also worth noting that's whats considered fast in central London (~30 - 40 mph) would be considered average (for a town centre) or slow (for a main road) in most of the rest of the country (granted there is more traffic on London's roads and they are often a bit more cramped). I certainly won't disagree that quiter roads are more pleasent that major ones, though!
"Your cycle and walking journey becomes longer (more effort)"
At King's Cross, for instance, the added distance is not a lot or nothing, depending what direction you're travelling, for cyclists and buses (it's a little more for cars) and not that much extra for pedestrians either. Anyone for whom a couple of hundred extra meters (at most) is too much efford definitely needs to be cycling! :p
"and requires negotiating more junctions (more exposure to risk)"
But I'd argue each junction in a gyratory is lower risk due to the more limited options/directions of traffic flow and lack or control of conflicting traffic. So, at worst, the risk is probably the same overall.
"Regarding cycling the effect can be mitigated by exempting cyclists from the gyratory operation. For large gyratory systems (e.g. Kings Cross) this would require substantial infrastructure which in the end wouldn't help pedestrians very much (vehciles would still go fast, bus stops would still be in the wrong places)"
This, I guess, is a sad side effect of the fact that London was never designed, it just grew. But (to use the example of King's Cross) - with a little local knowledge it is possible to bypass the gyratory. For instance I travel daily north-south past King's Cross by bike (from York Rd. direction). Southbound I can (and do) bypass the gyratory entirely by taking a faster and more logical route around the back of KX and SP stations. Northbound there is a (mostly off road) route, that is probably about the same distance, I could use to bypass the gyratory if I wanted (I don't usually use it as I think it's slightly slower and I don't mind passing the gyratory (well really, heading south from Euston Rd. to York Rd. you sort of avoid it anyway...). Similarly I used to frequently travel east from KX to Liverpool St. and, once I knew the area, I found a better route anyway).
Surely then the problems surround routefinding/route discovery for cyclists rather than infrastructure solutions? (Granted, that won't help the pedestrians). I'd think these alternate routes are better than redesigning the junction since they're more on quite roads (redesigining the junction won't magically reduce the amount of traffic on Euston Rd.) and often more logical routes (if you tailor-pick a route for your chosen journey, anyway). Of course this would benefit regular commuters more than one off visitors but (I could be wrong here) I think that's the majority of people cycling through anyway.
I find junction such as the junction of York Way and Goods Way heading north (near KX) far worse than gyratories (this being the junction on my daily journey I least look forward to) (In this case it's the risk of being left hooked/aggravated car drivers behind you when you use the correct filter lane to eliminate that risk - the fact that you're passing up an incline doesn't help, either. When I used to pass through the centre of the gyratory system more frequently while heading back to KX from Bishopsgate I never used to find the KX gyratory nearly as bad as, say, trying to make a right turn from Wormwood St. onto Bishopsgate (http://goo.gl/maps/fWbZ) at a standard crossroads of 2-way traffic - having to wait for conflicting traffic before being able to complete the turn, without a dedicated filter phase on the lights, didn't help there.
wrt infrastructure I think tfls past record of cycling provision shows that they can't be trusted to design decent, safe, sensible cycling infrastructer (I know, this is something LCC campaigns to change ;)). I'd rather nothing was done with these junction than the tfl engineers let loose on them with the brief to build some cycle paths!
I've always found with the gyratories that, so long as one know where one is going and gets one's lane discipline correct, you can't go far wrong. (If you do make a navigational error and/or end up in the wrong lane often the best thing to do (other than cycle a detour) is just to pull up at the kerb, get off and walk back to a convenient point to rejoin your intended route. It's not really disproportionate effort (and far lukier than an unfortunate car driver who has to go all the way around the gyratory again if he makes the same mistake...)
Well that my experience and my 2 cents, anyway. I'm afraid I'm still not convinced that a gyratory is any more dangerous than any other form of junction with an equally heavy level of traffic.