LCN Route 3 is a cycle route that mainly uses quiet backroads to get you into central London from the southwesterly suburbs.
Using backroads is usually a good strategy, because they tend to have low traffic volumes and often traffic calming to keep vehicle speeds down.
However, the real bugbear is that minor roads almost always have the priority against you. In other words, any time you get to a junction, you have to give way. Lots of Give Ways really slow you down. They make cycling unattractive and more dangerous because unless visibility is good, you have to slow down considerably or risk not being able to stop if there is any traffic on the major road.
So the logical thing to do if you were designing a system of backroads as a cycle route is to change the priority to favour the cycle route. Simple and obvious...except if you're a traffic engineer. You can always rely on them not to have considered the effect of junction priority on cyclists. There's one exception which shows it can be done: Meadow Road now has the priority where it crosses Fentiman Road, which favours cyclists (you still have to watch out for vehicles encroaching or failing to give way, of course).
In Clapham, there is a series of junctions on Route 3 where the priority is against cyclists. Here's a map of the area:
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Here's the first junction. The Chase is a wide but very quiet road leading north from Clapham Common. It really ought to have a segregated path. Route 3 going north then turns right into Hannington Road (below).
Going the other way you turn left from Hannington Road into The Chase, but your vision is obscured by parked cars, so you have to slow right down. The logical thing would be for the cycle route to have priority. Bear in mind there is little traffic here so there would be no real issues with this. You could build out the pavement south of the junction to shield traffic coming from the left.
Just a hundred metres further on, there's a staggered crossroads, where Lambourn Road crosses and the cycle route goes straight on from Hannington Road into Broadhinton Road. Again, the priority is against the cycle route and again without good reason as there is little traffic on either road. (below)
Another two hundred metres further on there is a major junction, with North Street.(below)
No surprise the priority is against you here, but there's no attempt to make life easy. No central refuge, no mini-roundabout or lights, nothing. You can wait a long time in rush hour before there's a gap in both lanes of traffic big enough to allow you to get across.
Another 70 metres further on, another crossroads. Again both roads are quiet but the priority is against you with no good reason. (below)
Next, in another 140 metres, we have Turret Grove junction with Rectory Grove. This is a T junction so the priority is against you. It's easy enough to make the left turn going north, but going south you have to make a right turn and there is a ridiculous piece of road design to make this as difficult and dangerous as possible.
First, Turret Grove is no-entry to motor traffic, and this is enforced by an island with a narrow cycle path through it. (below)
This arrangement causes the following problems:
1. You cannot make the right-turn at any speed even though visibility into Turret Grove is good. The cycle path is both narrow and at an acute angle. So you have to slow down and you're more likely to be held up by oncoming traffic, which increases the chance of being rear-ended.
2. You end up in exactly the wrong place in the carriageway, invisible to traffic coming up Turret Grove, and yet forced into the middle of the road by the parking bays you can see in the above picture.
So in summary, the road designers have done nothing for cyclists, except one thing that has made the road more dangerous. Now a couple of give-ways aren't a problem, but when you have give-way junctions with this frequency, it really starts to slow you down. That's when impatient cyclists start to take risks.