I have to say I have mixed feelings about this (I’m a Libra, what did you expect).
I live in Epsom and know that stretch of road well having driven it a thousand times and ridden it about half that number of times on both MTB and skinny tyred road bike.
I don’t like the thought of cyclists being banned from certain roads (other than motorways) because it sets a dangerous precedent.
But I have never ridden that section on the road, I always use the cycle lane (both North & South) out of a sense of self-preservation just because it’s so bloomin’ dangerous. I do tend to sigh when I see roadies (for it’s rarely MTB’ers), riding along that section of road although I fully accept that they have every right to do so.
The riders who chance crossing the fast moving traffic as they dart out from Westhumble Street frankly just scare me. It’s much easier to use the underpass
Oh and I’m not in any way a nervous rider, I cycle-commute 36 miles a day into central London and back including such perambulatory delights as Tooting High Street (the closest thing to a shoot em up video game in real life you will ever experience), Clapham Common, Elephant & Castle, Tower Bridge and/or the Embankment so I’m comfortable in traffic.